Okay, I've played some more today, so I'll give some more detailed impressions.
First of all, speed. This game is really fast. Not just in terms of player movement [which quite high], but also in the way that the game forces you to be in constant motion since health doesn't regenerate. You either need to be finding pickups around the map or getting glory kills on enemies to turn them into a health pickup fountain. Doom also pauses very infrequently for things like dialogue or cut-scenes [all of the later are still in first person, ala Half Life 2]. The glory kills are pretty cool, and I'm not tired of them yet, and they're also done very quickly to keep the action flowing fairly smoothly. And don't expect any long-winded dialogue or cut-scenes building up to the "start" of the game, it pretty much lands on two feet and takes off right out the gate. It really does feel a lot like the original Doom in this regard: fast pace, few pauses from the action except for when you want to do a little exploring for secrets.
Second, the combat. Like the original Doom, you get a wide variety of weapons to dispatch demons with and so far it looks like all the classics are back. They've done a good job here of keeping each gun relevant even when you get newer guns, through the use of various weapons mods, mod upgradibility, and the relative scarcity of ammunition [particularly during some of the bigger battles]. All the guns have a good feel, too, and each has a bit of uniqueness that makes them better suited to certain fights and certain enemies. Like Rage, enemies, especially imps, will exploit the environment to gain an advantage over you, constantly climbing around on walls and getting up to higher perches from which to lob fireballs. You can either try to shoot them from a distance or use the ledge climbing ability to get up to them, either works. One thing that some people were worried about early on is the number of enemies you fight at once, but that's really not a problem at all. While most of the time you'll only be fighting about 3-4 enemies, certain areas serve as monster arenas, which pit you against a dozen or more enemies at once [here's where play speed and ledge climbing really comes in handy]. Those big battles really get intense, too, and I can how playing it at a higher difficulty than I am [basically, normal] can make them really tough.
Lastly, the graphics. Doom's essentially using a second-gen version of the engine that powered Rage, which I thought looked fantastic. A lot of people, though, had a problem with the low quality of textures, especially when viewed up close, and the lack of any shadows. id Tech 6 considerably boosts the quality of the textures, though not to the point of them being the greatest ever or anything, and implements an actual lighting system. There are moving shadows, now, and flickering lights! You don't actually have a light source in the game, so it's hard to tell exactly how versatile the lighting system is, though. Anyway, it really does look great [I'm playing on roughly Medium settings]. There's a lot of contrast between very bright areas like the Mars surface and darker areas like the UAC facilities, but nothing nearly as dark as Doom 3. Throw in lots of flickering lights, particle effects, and very large environments and you get an overall view that is very nice to look at.
Basically, this is what Doom 3 should have been but wasn't.