You should be able to easily snag what you are after for under $1,000; and that's about what I paid for mine almost a year ago; and I'm talking Australian dollars, which are worth less than yours. Basically, you'll be sweet-as with something around that relative price-range from Onkyo or Yamaha; or Sony of course. I have the most former, with four HDMI slots as outlined above, which is perfect for just about anyone. You'll have four input slots, and one output slot going back to the TV; simple enough. Full HD surround sound with everything you have plugged into it, with a click of a button to change between them. An extra click from your TV's remote if it's something like an Xbox/PS2 plugged in with component cables; which is like switching between the TV and 'AV' back in the day.
I have a 5.1 speaker setup, but they support 7.1 as well. The latter of which is highly unnecessary if you are in a small room like mine. Big open space? Definitely go for 7.1, if you have the space.
As for the TV, anything above $3K is going overboard, but again I'm talking in Aussie dollars, and that was about a year ago. I paid about that as my Sony Full HD came with a 'free' PS3 and five-year warranty. You should be able to pick up a top 116cm (46-inch) for less than $3,000 by now, and I'm talking Sony-goodness; even less for a cheapy-brand. Hope these figures are of some use to you.