I would first increase the budget some and then come up with a list of your desires. Don't set the budget without knowing the market for home theater projectors and what you want.
Seriously on that one. Your home cost a lot of money, if you intend to use the space to enjoy home theater (which is amazing) then plan to get at least an entry level projector which will keep you satisfied and happy for years to come. Not the cheapest thing which happens to fit your budget.
That said - right AROUND $1,000 you have some options such as the Optoma HD33 or the Epson 3010 which are worth looking at for 3D. The Epson 8350 is a solid model with great versatility, but no 3D, for about the same price.
You will need a screen and speakers as well to make it all work - those are extra.
You should do some more research on this. Read the reviews here and I am happy to help here, but projectorcentral.com and projectorreviews.com can provide some additional information.
What size is your room?
How is light control?
How is the room painted?
What type of content will you be viewing?
What screen size are you hoping for?
What is your viewing distance?
Do you want 3D?
Do you have any location requirements for the projector?
Lots of first level questions to go through before any real recommendations can be made, and you really should not be tight with your budget. Save up for a few more months if necessary to allow a few hundred bucks more if it gives you the right product.
