Ok, if he is like any other teenager or around that age then I'm guessing his room is rather dark most of the time? I from the time I was 12 to now an adult I keep everything dark and blacked out because I have a chronic headache issue where ambient lighting can't change a lot when I'm on the computer. (In case anybody was wondering, I'm not a dark cave hermit rofl).
This being said, you can do with a low lumens projector. What this means is, if the room is darker you wont have to have a crazy high quality high lumens projector to have perfect picture quality in the light or day time.
A good 1080p projector will cost between 700 and 1200 here in the US, and I'm guessing prices will be about the same only converted over there. Optoma, Emerson, Sony, and InFocus make good cost effective projectors in both 720p and 1080p (plus 3D in some).
To make things a little more cost effective for you, you technically don't need a roof mount or screen. Depending on the color of his walls you can project that bad boy right on the wall and it'll look fine. I'll give some examples of me playing Forza 4 during the day with only curtains blocking my sliding glass door. Pardon the phone camera quality. I should also mention, I have a cream/tan colored wall set.
My screen area is 120" at 1080p with a ghetto "roof" mount type system. There are ways of getting around a roof mount by using things from your local home improvement store. I can elaborate on that more if you want later.
Another thing to be very
careful over is native resolution
on a projector.
To give you an example of what I mean, a 720 projector will say native resolution or simply "resolution" at 1280x720 or 1280x800. If they say 720 or 1080 and the native isn't just that, then that means the projector will accept higher res signals and they will be downscaled. I made an example of the projector you linked.
Here is a projector that is 1080p native.
INFOCUS SP8600 Full HD Home Cinema Projector Deals | Pcworld
It is quite like mine actually.
See the major difference in price? It comes with a huge difference in quality too.
There are many many myth-truths with projectors for regular use.
#1 is bulb life. People claim bulb life is terrible. It isn't. Your projector will last "forever" as long as you take good care of it, keep it cleaned out (every 6 months or so dust it out like you would a PC), and replace the bulb. Most good projectors have a 3000-4000 life span now. I'm barely capping 500 and I have used mine heavily since August. Think about it this way, 649 for a projector then say, 200 for another bulb in 3-5 years. Or spend more on a TV that isn't as big and if it dies hope like hell it's in warranty or buy a new one at same cost or more. Makes sense to go projector.
#2 You need a completely dark room for good picture. No, you don't. I just proved you don't. The blacks aren't perfect but IMO if you wanted perfection and had the cash needing a dark theater room wouldn't be a problem. I can watch light shows like The Big Bang Theory, Pokemon, or whatever with a light on in the same room no problem. Movies I can watch during the day easy as long as no lights are on in the immediate room.
#3 You absolutely need a screen and roof mount. Again, no you don't. I just proved it. Sure to get the opportune picture you want those but you can get your good quality projector now and get the rest later if you feel you want it. That's what I'm doing.
#4 You can get an equally as big TV for the same price. Complete and utter BS. My projector will do 300" at around 20ft of throw. Last time I checked, no consumer LCD 300" 1080p TVs in the market. Right?
#5 You can't plug everything in to it. Sure you can! I have my PC, Wii, and 360 hooked up to mine right now. Ever played Zelda Skyward Sword on 120+"? I have and it's amazing. So is any racing game as well as Halo.
An easy way to do this to reduce cable clutter is get a cheap HDMI capable A/V with passthrough. All signals in one box, one HDMI cable goes to your projector for video.
I hope this explained a bit about projectors to you. I absolutely love mine, and anybody who comes over to my home wants one. Simply because they are amazing and the closest "theater" like experience you'll get at home. TVs can suck it
BTW sorry about the wait. Valentines day and all.