As a certified cheapass when it comes to all facets of my life, TV's are a great find for any budget minded shopper. You missed the 2nd best time to buy a TV by two weeks as TV's go for super dirt cheap over Thanksgiving.
Your #1 time to buy TV's are the two weeks leading up to the Super Bowl, so basically, if you don't jump the gun, you're about two months away from spending that $800 on the biggest TV it'll buy.
Now for some realities...
For $800, you're looking at rear projection or CRT if you want something larger than 25". Plasma and LCD go up in price pretty quickly once you get over 19-20"
You might be able to do as well as scoring a DLP Rear Projection TV for that price, probably something in the 34-42" range. Super Bowl TV sales are awesome and they have stupidly affordable deals during that time. You might also consider using some of that $800 as a good 1/2 to 3/4 down payment on something "outside" your price range. You can take the $800 and it'd basically be another $800 - $400 for a really nice LCD or DLP TV.
I wouldn't recommend a front projector, as the cheaper (sub $2000) projectors either compromise on image clarity (it's called the screendoor effect, because that's what your video looks like it's being seen through), lamp brightness, or missing features (no internal sound!)
CRT's are excellent HDTV's and have an easy 20+ year lifespan if well tended to and bought from a reputable manufacturer (until recently, I had a 9 year old Toshiba that had impeccable quality, especially for a 4:3 27", and looked better than my own parents 4 year old 60" HDTV)
Rear projections look excellent, but they have to be adjusted for color separation issues. Most rear projection images are based of
3 projectors throwing red, green, and blue images at the screen. DLP solves this by throwing the colors up with a rotating device to throw all three images up with one output. The colors can look cleaner and brighter than older RP technology, but there's a persistance of vision effect, where if you turn your head really quickly while watching the TV, you'll see the image separate into Red/Green/Blue and then return to normal. It's distracting on different levels to people, and some can't stand it. Personally, I don't care, since it looks great when you're watching.
LCD is the ideal #3 choice, they have thin profiles, smaller sets having ALL the features you're looking for, some with built in features that CRT's abandoned long ago in favor of making the last generation of CRT's all HD friendly as quickly as possible. (LCD's with built in HD upscaling DVD players? CHECK!)
Component cables are the way to go, as the colors are cleaner and look sharper, because of the increased color quality available in each R G and B cable. First movie I ever watched in component quality was Airplane!, and it was like watching a modern film. I can't watch a movie in composite anymore.
Dude, in all seriousness, look at how old you are to judge what kind of TV you should buy. You're a guy who plays games so use this as your slide rule on what to buy.
Under 13? You don't have $800. That's cute to say you do, and we really do believe your Grandmother gave you the money, we really do. Every 12 year old braggart worth his salt will try the old "my parents gave me a credit card" line, but now with debit cards, this is easily struck down.
13-18? For $800, go get a nice 27" 4X3, spend the rest on games, you've got Shmups/Japanese RPG's to consider as well.
18-23? You're in college/unemployed, you don't have $800, you have credit and massive debt. You either have the 27" you stole from home when you had money, or you have someone's abandoned older rear projection you bought off of Craigslist as broken and repaired for $100, and you are a god in your dorm/apt building.
23-27? Assuming you didn't get married or are not in debt up to your ears from college and rabid iPod buying, you take the $800 and invest in a 30-40" TV, HD isn't a concern if price is the factor, because while HD wows, only your male friends care, and you all likely go over to another older friends house who has HD and a projection TV/Plasma/etc.
27-35? If your wife/GF isn't spending the $800, you've got the pick of the litter. Spin the excuse for a larger TV on any onset adult problems (vision "my eyesight's going" works perfect, as does "theater prices are so expensive/theaters suck/etc. " It also helps if you have kids as all large screen TVs have the ability to play back Disney and Nickelodeon TV shows with stunning clarity. This results in hypnotized children, leaving you free to go play games on your own 25" TV in your study, all to yourself.