I feel that the best way to describe it as a whole is to describe it in the sum of its parts. Therefore, I'll go cutscene by cutscene and level by level.
However, for those who really don't give a *** what I really think (may apply to most), the TL;DR version: It's pretty good.
First of all, it can't be said enough how beautiful the cutscenes are. As a long-time Halo fan, this doesn't really say anything new except that Harvest, like Reach would be, is only partially glassed. We are also introduced to the three main human protagonists: Sergeant Forge, Professor Anders, and Captain Cutter. Like most characters in the Halo series, you can pretty much tell what kind of character they are based on the first few lines of dialogue. There's very little character development throughout the game, as the gameplay itself was given the starring role. While halo Wars couldn't possibly be described as a complex game, I feel that it makes the most out of what it has.
From here, we get to the first level and the first objective of the game: secure Apha Base. We begin with Sergeant Forge in a Gauss Hog (why do so many people have a big problem with the Splazer in this game and not the Gauss Hog?) as he rendezvous with other UNSC forces to recapture the base. This level is great for getting the feel the game and also teaches us all a fundamental strategy: There's not Covenant force that can't be broken with the right amount of Warthogs.
After this very simplistic (and criminally short) level, we see another wonderful cutscene, introducing the Arbiter. Right off the bat, the cutscene ensures that we know he's not the same Arbiter by being as big of an *** as possible. We are also introduced to the Prophet of Regret, whose youth hasn't made him any more personable or better looking. However, it's nice to hear Robin Atkin Downes reprise his role. From there, we have the level that everyone got to see in the pre-release footage. It feels like a tutorial level and, sadly, still plays like a tutorial level. And, while the level's sidequests can lengthen it, the actual objective takes no longer than 5 minutes to complete, destroying the insanely oversized detonator.
From here we see Anders and Forge get themselves in a lot of trouble as shieldless Stealth Elites (a la Halo 1) were ready to ambush them and their marines the moment they activated the relic. The Spirit of Fire sends down two Grizzly tanks (Forge's pet project? He made those freakin things?) to clear the way. Unless you're playing Legendary, this makes the first half of the level a shooting gallery. The rest of it is essentially an escort mission going back the way you came (with the exception of a bridge or two). After this, we depart from Harvest to something a little less familiar to the Haloverse.
As soon as the level ends, we discover what the mysterious relic of the infinitely mysterious and powerful Forerunner truly did: point us to another planet. Looking at the cutscene, I'm not sure what made them think that the multiple lines went to Arcadia, but okay. We say goodbye to Harvest to travel to the beautiful (well, not in the fifth level) Arcadia. Cutter enters in the midst of a battle between a few Covenant ships and UNSC ships ( one of which is very familiar). As usual, humans are getting their asses kicked, but the Pillar of Autumn is once again showing that it has all the moves required to tango with the covies. From there, Cutter sees footage of the fight on the ground and... recognizes Spartans (?), so he sends Forge down to help evacuate civilians. This level is frustrating, especially on Legendary, but I love it. Essentially, it's a "Defend this mission for 20 minutes". The Spartans are AI controlled and are, at best, inconsistent. Sometimes, they can handle everything. Other times, they just stare blankly while Covenant forces destroy the evacuating ships. Also, in a choice of bad level design, the cowardly *** who pilots Cargo 3 is always destined to die, whether you save him or not. Thanks for telling me, Ensemble. I'm glad I wasted 3 Hornets protecting that dickhead.
Once the civilians are out, Forge and Spartans run like hell to the outskirts of the city, where they set up a base and build up until the Covenant base in the corner can be taken out. This level is pretty standard in RTSs, except for the added twist of Spartan Group Omega making an appearance. Who these Spartans are and what they do after this is never explained. After this level is over, the game gives us another shiny cutscene.
Cutter tells us that the Covenant have put up a shield over a certain area. Well, at least now we're getting back to the narrative, right? I mean, the Covenant put a shield over it for a good reason. Maybe they found another artifact. Wait, what's that? The Spirit of Fire can shoot through it? Okay, so it's not a shield. More like a plasma... curtain. Oh well, we get to play with a prototype Rhino tank, a cause for a lot of the cries about this game breaking canon. I still don't get why the Plasma Rhino gets a lot of hate. The UNSC had a lot of exotic weapons. Hell, 30 years before the Covenant War, they had an Anti-matter rifle. With weapons like the Gauss hog and the Spartan Laser, I don't see how this weapon seems to be getting all of the hate. Besides, it sucks at taking out anything except for these plasma curtains, anyway. The mission itself is pretty straightforward: build base, build fortifications, build Rhino, send it to wherever the hell Anders tells you to. As a nice bonus, we get to use the Spirit's MAC gun to take out a Covenant base. As a nice touch to ensure that even an enormous dumbass couldn't fail the mission at that point, they give you 40 shots. Personally, I would've just taken one shot from an actual MAC than 40 from the piece of crap MAC the Spirit of Fire gives you.
Before this mission, we are once again shown the Aribiter and Regret, this time face to face in a mysterious cloudly place known as the Apex Site. There, Regret, in the presence of Honor Guards (who are missing their fancy hats) reveals the plan. A little different than lighting a holy ring, but it's close enough. Given that Regret, according to the backstory, was there before the game began. Therefore, what was on Arcadia that was so interesting? Why bother with the plasma curtain? How many licks does it take to reach the center of a tootsie roll pop? The world may, and most likely will, never know. The game won't be explaining it either, and hopes that you're too distracted with the next mission to ask any questions. The Super-Scarab is, IMO, the best level in the game. If not for an exploitable glitch, this level is challenging, encourages micro-management, and keeps you on your toes. With this level, we depart from Arcadia for some less interesting missions.
Forge and Anders are shown in the following cutscene. Neither one of them, nor the emerging Arbiter, attempts to develop themselves further as a character, sticking to their archetypical roots. Spartans arrive just a bit too late, but looking badass all the same. They jump on board the Spirit of Fire and debate whether to follow Anders or not. Thankfully, they decide to follow before the ship goes faster than light speed and find the Shield World, along with a very angry looking Elite Combat Form. The cutscene really kicks ass and makes up for the crappy level that follows. First of all, beyond adding few new enemies, was there any point in having the Flood in this game at all? Canonically, they make sense. However, they play no role other than a meaningful distraction for three levels. However, I have another problem with this level: Brutes. First of all, even though they're with Grunts, Serina doesn't consider them Covenant? Second of all, they had no reason to be there other than fanservice. Elites could've been there and it wouldn't have made any difference. Hell, no enemies there wouldn't have made any difference. Thanks to hero units being almost impervious to Flood ground units, any threat the Flood provided are nullified by sending Forge and three Spartans after them. The Flood, compared to the Covenant, provide little challenge. Only a few flood units even pose any sort of threat.
The next mission is pretty standard. Reach Red Team and kill the Proto-Gravemind. Once you get Hornets in the air, this level's pretty much over. In between fighting the Flood, we get to see the Arbiter and Regret looking over Anders before being informed that the UNSc has arrived. The Arbiter, to prove is evilness, punches the messenger and orders Regret to GTFO. Meanwhile, Serina accidently talks to the Shield World's AI and the Shield World's sea begins to part. The Shield World level provides a nice twist: fight through the Flood and save as many people before the Spirit of Fire is sucked into the planet. If you have the right places cleared, you can use Gremlins to short out the pylons and buy more time.
Thankfully, after the Shield World mission, it picks up. No, still no more Covenant, but we get a nice twist. On board the Spirit of Fire, as it goes inside the planet, Sentinels and Flood begin to take each other (and you) out. Cutter gives one order, as badass as he gets, telling you to "Get those things off my ship!" The level also provides a good oppurtunity to practice micro-management (or as much as you do in this game) by insuring that Flood colonies remain dormant.
One the hull is clear, we see the entrance of the Shield world. It's like a Halo if it went around 360 degrees. The view is then disrupted by Regret's fleeing ship, which stops for a while to trade some shots with the Spirit before getting out of there, leaving the Covenant forces remaining to fend for themselves (or catch a ride on one of the sweet-ass Forerunner ships). This level is also a nice twist, using Cyclops to repair the Spirit while other forces defend from Covenant forces boarding the ship.
Getting back to the Covenant side of things, the Arbiter uses Anders to activate the Apex Site, making a triumphant speech and disregarding the fact that they let their human puppet get away. Anders, using the Forerunner's magical "Do whatever I say" machine, is teleported to the perfect place to be saved by Forge. The next level is fun, and not just because you can go on a rampage in a Scarab. Seeing the Flood begin to take hold in the interior of the Shield World finally begins to show the Flood's threat. While at the beginning, the Covenant are far more imposing, this changes as the Covenant begin losing their bases one by one while the Flood colonies regenerate, usually stronger than before.
Now that everyone's back where they should be, Anders reveals her plan. Sacrifice the ship's FTL drive, overload it inside the Shield World's sun, and blow the whole place up. Besides dragging an Elephant and the FTL drives around, this level is pretty fun. The Flood, somewhat threatening in the last level, are back to being a mild nuisance at best. Sentinels, likewise, are little more than an annoyance. After this level, you get a very badass cutscene. Once again, the Arbiter shows us that he's overly arrogant and really needed shields. The hat-less Honor Guards are now replaced with Blue shieldless Elites. This allows Spartans and Forge to kick serious ass without much injury. After the Arbiter's death and his corpse is disposed of, forge makes a heroic sacrifice to let the others escape. Thus, we begin the last level, the aptly named Escape.
This level gives you everything you could hope for. You have all of the leader powers, all of the upgrades you could want, and all of the Scarabs popping out of nowhere and blowing up your bases that you have wished for. Open some locks and fly the Spirit out of there, where it flies home at slower than light travel until the cliffhanger implies something has happened.
Overall, the game's breaks from the canon are reconcilable. Sure, the UNSC isn't supposed to kick all of the ass, but a game where you lose all of the time would be even worse. The only truly unforgiving thing I can really are that the Spartan have energy shields (no excuse for this one), the Flood can make Grunt and Jackal combat forms (Maybe the Flood on the shield world behave a little differently or decided to experiment), and that the Covenant have first-hand combat experience with the Flood predating Halo (maybe Regret told them to STFU). I believe that the rest are pretty blown out of proportion. The "Spartan paradox" existed even before this game. Nylund screwed up the Spartan numbers long before Ensemble did it. The Spartan Laser in Halo Wars could easily be a prototype (a la the Battle Rifle) or even just an earlier model (where does it say the Spartan Laser was new in Halo 3?).