I usually come the other way and set about making a room dark when the client needs it.
Anyway second hand projector is an odd one -- if it a bulb based projector then do look up how much bulbs cost. They do not have the best lifetime and they are not the cheapest to replace when they do go wrong. Likewise projector bulbs can be even worse than printers when it comes to the thing wanting the exact bulb and nothing else.
If it is a second hand LED one then that is doable. There are some cheap and cheerful Chinese models (
http://www.eevblog.com/2014/10/08/eevblog-671-white-van-speaker-scam-teardown/ 25 minutes if you do not want to watch the lot).
If you have got cash for this one then business projectors are typically the brighter offerings (they have to work in meetings after all) but they might not have the best colours.
Alternatively if you are going for old games is it not worth hunting down a later CRT with component inputs?
If you are really bored then the N64 has a pretty nice RGB mod you can do, I already said my bit about the Wii and component in earlier threads.