No you wont be able to use a keyboard/mouse with the 360... at leas not right now.
Don't bank on a 3rd party adapter ether because MS is requiring certification of all 3rd party products and is making use of a security system that will only allow certified products with the appropriate chip to work with the Xbox 360.
MS has said that USB keyboards will work in the 360 but only for text entry with certain supported games, there are no plays for or to allow mouse support for anything right now.
As for your HDTV... I'd recommend checking out the 360 AV forums section, there's a substantial topic on which TV to buy.
Personally I'd recommend a CRT based set over any other technology. they're cheaper and they have a better picture. I recently did quite a bit of research helping a friend buy a new set and I like the Samsung the best. With that said Best Buy has a 26" Samsung on clearance for about $400-$600 depending on the store. If you're lucky Target had a similar set on clearance for $350 or less (depending on the store), though most are sold out at this point. If you want something slightly larger most 30" sets will be in the $1000 price range.
If you absolutely NEED a flat display because of space I'd recommend the Aquos LCD over anything else, but I still like the picture on the CRTs better.
My guidelines for buying an HDTV:
-widescreen 16:9
-native support for 480p, 720p and 1080i
-DVI or HDMI inputs with HDCP
-good response time
^ that will weed out A LOT of sets past that just go by picture and price based on your preferences.
AFAIK NO manufacturer lists a response time for their set, it's something you have to test in person, and can make a fantastic looking set completely useless for gaming. Some sets have slowdown in the conversion process so the picture appears 1/2 second after it receives it. This is fine for TV and movies but gaming relies greatly on fast response.