So, from what I'm reading:
1: You've got a little bit of ambient light at times and you'll probably want to view in the day occasionally.
2: Your viewing distance from eyes to screen will be about 144" (12').
For a viewing distance of 144" (12'), I'd recommend a 106 or 110" screen (at the minimum) based on the viewing distance calculator @ http://myhometheater.homestead.com/viewingdistancecalculator.html
That's the minimum screen size to achieve a THX viewing angle. You could go bigger, of course, but then going too big could make your wife mad or maybe tire your neck out from looking back and forth too much while watching TV or movies.
The electrical being 6 feet away from the screen isn't so bad of an issue, but I would recommend mounting the projector just above or a little behind the viewing seats so the projector is not in your vision. You could either run the electrical from 6 feet or the back wall to the projector. (Could use wall channel on the ceiling to make it cleaner looking, if running from 6 feet... but I'd just run it from the back wall to the projector. Since I'm assuming the projector will be above the seating area, 12' from the screen, and the back wall is 15' from that, it's only a 3' plus some change cord run.)
I guess, you'd want to get an electric tensioned projection screen, as well... Whether you get it in white or grey is up to you. White is better all-around, but grey usually has higher contrast and works a little bit better if you're going to have ambient light in often. If not so often, go with white, as it's a more uniform picture... you can use the projector's "Bright" mode to compensate when you're watching in the day with the blinds open.
If you got an Elite Screen CineTension 106" grey screen (TE106HC2 on Amazon), it'd run about $1.1k where as the white (TC106HW2) runs about $860.
You'd want a tensioned screen so that the screen comes out perfectly flat, without wrinkles, and doesn't sway in the wind due to air conditioning or anything else.
Being your budget is $2500 and, JUST ASSUMING, you get a grey screen, that'd leave you with $1400 for a projector. (Not including the price of your ceiling mount...)
People say DLP gives the best "film like" picture, but also better for motion and what not as well. Problem with DLP, when not using 3-chip DLP which is tens of thousands of dollars, is that some people can be sensitive to the "rainbow effect"... where you can see the color separation the color wheel does on the picture... if you're not susceptible to it, I'd go ahead and nab an Optoma HD131Xe projector. It costs around $750 and gives a decent enough picture. The throw is perfect for 106" at 12' (144").
If you don't MIND, though, I'd REALLY go for an Optoma HD25-LV. It's $1079.99 and has twice the light output of the HD131Xe... (Not that the HD131Xe is dim at all, but more lumens is always better, especially when you're dealing with ambient light, and you can tone it down using the "Eco" mode on the projector if necessary.)
If you're susceptible to the "rainbow" effect, then I'd advise a 3LCD projector. Models you should consider would be an Epson PowerLite 3020 ($1499) or an Epson PowerLite Home Cinema 8350 ($1269.99)
3LCD can still put out an amazing picture and, actually, contrast of 3LCD projectors has now exceeded DLP as has the color accuracy. Only problem with 3LCD is probably motion. It's not as clear as DLP but still very acceptable. If you've ever used an LCD TV and turned off that "Soap Opera Effect", that's how your image would look on an 3LCD... 'cept probably much better contrast and color. There ARE 3LCD projectors that feature the "Soap Opera Effect" (Frame Interpolation), but they generally cost quite a bit more money.
The prices I'm getting are from Amazon, you may find better deals elsewhere... but all of these projectors will comfortably throw up a 106" from 12' (or even closer or farther) and they're all 3D EXCLUDING the 8350... The 8350 is the only one that cannot do 3D.
Finally, you'd have to find a mount that looks good for you for the projector... There's a ton online and I think it's mostly up to aesthetics...
I suppose that's it as far as my suggestion on things.