DLP, I would recomend the Optoma HD700X (its a ~£400 projector and crisp image)
Second hand isnt advisable, as there's no garuntee on lamp life, and you could end up spending another £100+ on a lamp within a week.
Life is a tool, use it wisely and properly. Don't break it, because you can't exchange it if you do.
Life is an instrument, it needs regular cleaning, maintenance and tuning to keep it at its best.
Fear, is not knowing. Terror, is finding out.