Most on these forums do not recommend the HTIB route. Basically because the quality of the speakers leave a lot to be desired. If this is going to be your primary listening system I would suggest going with a system of seperates.
Generally most here also suggest spending the higher percentage of your audio funds on the speakers. You get the most bang for the buck on the speakers rather than the electronics.
I do not have a lot of listening experience with the many brands of speakers out there but can give you a suggestion regarding the Paradigm brand. One pair of Titans ($220 US) for the front and a pair of Atoms ($200 US) for the surrounds. This leaves you $380 to $580 for electronics. You can buy a very nice budget receiver from Pioneer, Onkyo or Yamaha in the $300 range that will provide good power and decent features. The left over money should be set aside until you have enough to buy a subwoofer to match the speakers. You will need around $400 US for a nice sub.
I purposely left out the center channel because its' duties can be handled by the fronts until you have extra funding. If you go with the Paradigm brand the CC170 center channel is quite nice and is around $200 US.
Your best bet is to go to your local stereo/HT shop, bring a favorite DVD and some favorite music cd's and start listening. Speakers have their own sound and our ears hear that sound in different ways generally so what may sound great to me is not as great to another.
The receiver is the easiest part to change. While it has impact on the sound it does not have the impact of the speakers. Also receivers drop in price as newer models become available so in a few years, or less lol, you can upgrade the receiver and have a nice backup/spare to use in another room or sell if you want/need to.
I have no real suggestions in the TV area. I have looked at a lot of models at BB and elsewhere and I see you get what you pay for. An inexpensive LCD or plasma is exactly that, inexpensive and the picture usually matches the low cost. Both have their pluses and minuses which you can read about in some of the links provided below. Again my recommendation is to watch them and choose the model that gives a picture that you like best. Many people have their issues with BB and other big boxes but they do have the most models/brands on display all generally showing the same loop of video, albeit it is high def and does not show the picture quality of standard signal but possibly the salesperson can change the signal type on a tv you want to view in standard mode.
Good luck, tell us of your experiences and enjoy.
Links:
http://www.paradigm.com/Website/News/news2.html
http://www.onkyousa.com/prod_class.cfm?class=Receiver
http://www.yamaha.com/yec/avreceivers.html?CTID=5000200
http://www.pioneerelectronics.com/pna/v3/pg/album/compare/0,,2076_310069809,00.html
http://www.soundandvisionmag.com/article.asp?section_id=13&article_id=1127