I would avoid trying to tilt your projector if at all possible as that will require you to use keystone corrections to fix the distortion. How big of a project is it to move a mount or get a new mount if you have to?
If you are concerned about a screen being too bright with a certain projector, don't forget that you can always add an ND4 or ND2 filter in front of the lens to kill some of the lumens.
I agree that used projectors can pose a risk, but keep in mind that some of the cheaper new projectors only have a 1 year warranty anyway and warranties on bulbs are commonly 90 days. My first projector I bought used and lucked out. I only replaced it because it was an entry level 720p model that had a not so great contrast ratio.
However, it can be very easy for someone to fake the hours a bulb has been used and not all projectors separately track how long a bulb has been used in ECO vs the bright setting which could greatly impact bulb life. So, I think the key to buying used is that you buy from someone you can trust and try to seek out models that have a history of reliability (which is the one big benefit to buying used in that you know the track record for your specific projector model).
Another thing to consider if you are on a real strict budget is that many different projectors have very different replacement costs for bulbs. My current projector, a HD131xe, has a bulb that can be found for $150ish, but the prior model I believe cost about double that for bulbs.
One other final thing on buying used, if you decide to do it is be patient, flexible, and willing to buy the projector at a moments notice. I would have a list of projectors you were considering and a price range for each and be willing to pull the trigger if the buyer seems trustworthy.
Now, one alternative that you may want to consider is going for something refurbished. That often gives you a warranty, but may not give you a new bulb in all cases. Every so often deal sites like woot etc will get a shipment of refurbs in. So again, have an idea of what you want and then be ready to pull the trigger as soon as you see something that meets the criteria.
You can definitely find something you will be happy with in your price range whether it is used, new, or refurbished, but as it is a low budget, I would familiarize myself with the low end models that were released in the last 4 years and eliminate ones that you are not happy with.
I would also keep in the back of your mind that some really good current gen projectors had gone for $600ish refurb (the W1070 and HD25e in the last two months) so I would try and stay within your budget or if you do decide to go above it, go all the way and wait for the next refurb deal on the W1070, HD25e, et al) rather than spending an extra $100 and getting an older 720p model.