There is a long list of projectors which will meet your needs but we need to clarify some items...
1. You need to break down your budget... $5,000 for projector? Or, $5,000 for projector, screen, speakers, receiver, Blu-ray Disc, cable, rack, cabling, etc. Your ability to get a nicer projector slips dramatically if you have a lot of other expenses which go along with that budget.
2. Are you planning to do the installation yourself, or hire someone? An in-wall installation and setup can take a couple of days to do properly - and typically runs in the $1,500-$2,500 range depending on the installer.
Without really knowing this stuff, I will assume you have a flexible budget (somewhat) and want gear which is very good, but not necessarily top of the line, and to that regard the Epson 6500UB or the Panasonic AE3000U are excellent projectors for a bit under $3,000. The Epson 6100 is pretty solid around $2,000 and Sanyo has a model in the $1,500 range which isn't to shabby. All these projectors are LCD and have very good versatility in their lens and setup options and are all 1080p models.
If the room is dark - as in no windows and you intend for it to be a theater, then you MUST pull out a paint brush and get the walls and ceiling painted down to a nice dark color to reduce reflections. You will be fine with almost any screen if you do this.
For a screen, I would follow THX standards if you like sitting in the middle of your local movie theater. That typically means that the width of your screen should be about .66x your viewing distance. So, if you are sitting about 11'-12' from the screen, a 7-8' width or about 100" to 110" diagonal screen is appropriate.
I would go with the Carada Criterion in Brilliant White (1.4 gain) to give the projection solid punch.
Keep in mind, you will want to check the projection calculator at Projector Central to ensure that whichever projector you end up with it will work with the screen you get. All projection calculations are from the LENS to the screen, so a projector which can hit a 100" diagonal from 12' away, but the projector is 18" deep, won't work because you would need a room about 14' deep to accomodate it.
If you want a 100" diagonal, from 11' throw distance, you have over a dozen choices available to you with projectors from $1,400 to $3,500 and while none of them are lousy, I would stick with some of the more typical manufacturers including Sanyo, Epson, and Panasonic. Really though, none of these are lousy...
http://www.projectorcentral.com/projectors.cfm?g=1&hide=0&st=1&mfg=&p=500&p=3500&w=&r=13&br=&ll=&t=&db=&dt=&c=&ar=&dvi=&td=11&i=d&is=100&sort=$