To start with I love projectors and I think they are amazing bits of kit, some of the best gaming, film and TV experiences (especially with friends) I have had have been with projectors. However they are not without their flaws and one would be foolish not to recognise them and know them going in. As a simple response 2000-2400 euros will see you comfortably (not top end mind) in the market brand new (VAT/sales tax will be a killer in your parts though so consider a dodge if you can- the "for a few [currency] more" is even worse here than it is in hard drives, not sure where you are in Sweden but this is consider a trip across the water time) and if you know what you are doing you can probably swing something extremely nice on the second hand front.
The main one people will get hung up on are bulbs. These are not your garden variety house bulbs but high ends bits of kit that kick out serious amounts of light and they would probably make for a very good study on vendor lock in (remember printers circa 2000.....). This means cost of ownership will include a replacement bulb or three- lifetimes are in the sub 700 hours mark for most and for some more like 300 hours, brightness (that you normally set) is a big factor here though. I see a few with claims of 2000 hours and the like and while only have a few doubts about them "lasting" that long whether they will still look as pretty as that number draws closer is another matter entirely.
Some work is going on though to level this playing field if you are more electrically inclined:
http://hackaday.com/2009/12/22/fix-a-projector-on-the-cheap/
If you are considering second hand then that sort of thing you will want to be up on. Occasionally people throw "old" projectors (a commenter on that post mentions schools and indeed they are a source for many of these) for next to nothing that only need a bulb and a polish of the case but like everything else there are those who know all of this, businesses that are going under or that are otherwise upgrading or attempting to cut losses (projectors are not all that useful for many of them yet still cost good money).
Dare I say a quick read of something as basic as
http://electronics.howstuffworks.com/dlp.htm/printable might do some good here as well.
Next up comes types of projectors, arguably three main sorts.
1) Office
2) Home cinema.
3) Hybrid.
There is a further type in high end custom or application specific (most notably dual projectors for use in polarised 3d display) but this is a case of if you have to ask.....
1) Office ones are designed for meetings and to get data on the screen under something resembling ambient light or worse some sunlight. Colour response is usually not brilliant. You could probably have a great time borrowing one for a week(end) though.
2) Properly set up these look amazing, better than anything else you will see but like a good speaker setup it is not all in the devices but the room you are in and the actual setup/position of the things.
3) Going for a best of both worlds some companies have made things that are perfectly acceptable for both if you are willing to make a concession or two. I am not entirely current on this side of things but 9 months ago when I was last looking things were looking good here and a quick scan says it happened.
You have the usual input and output resolution (true HD is nothing special compared to a standard computer monitor but there are still a few models that top out at 1024x768 and 4:3 with letterbox as widescreen is still common), input methods (DVI and HDMI is actually relatively new: component and VGA held for longer than any other display method) but frankly if you are in the market for a new display device in this day and age you had better know all this already. Frame rates are usually not that impressive compared to monitors and televisions but assuming you do not get a toy you will be fine.
As an aside though while you can work around it manually having to tweak your projector mountings is never fun so if you can I would get some form of decent image corrections (keystone correction is the main thing for most people but rotational, pincushion and everything else you saw on your favourite CRT monitors back when is nice too). A quick scan of reviews should tell you of any problems with colours with rainbowing (the spreading of colours, think prisms) being the big one.
Still on this I have yet to see one with good speakers (about there with a good laptop at best, bad LCD TV at worst) but if you are not getting at least phono outs for your trouble or having it left to you to sort walk away as it is clearly a rip off going on.
A quick aside on sound, bulbs kick out a lot of heat and sometimes you have a fan that wants to tangle with it.
Projector screen- part of the colour response I mentioned earlier also includes blacks, some opt for a matt painted wall but the big boys will tend to have a screen. White is the traditional colour but for a good contrast projector grey is the new thing. While a few bolts of cloth will be near flawless cloth at that level it does not come cheap and neither really do screens. If you want fancy linear actuator driven screens like the house of your favourite rap star go right ahead but a simple pin up screen or roll up screen (think back to school) has no downsides from a quality perspective.
I have somewhat skipped over this one thus far which would probably get me strung up in certain parts of the projector fan crowd but contrast ratio and image brightness (usually in Lumens) is a thing worth noting, like any area/tech now reaching the masses you have idiots and zealots who know their little bit of info (ever had to explain speaker power, input power, clock speed, numbering schemes, horse power, torque, ram size...... to someone who considered it the be all and end all of a given field?). At a given point it is only good if you want to use it in a bright room/with the lights on/on a plain wall and if you are spending the kind of money you have said it will probably not be a problem.
All in all I do not see projectors outright replacing regular screens but for games, films, TV shows and some more casual computer use a projector can be had in your budget.
