What is a good projector in by budget?

I have been shopping on Amazon for an affordable projector. I would like to spend about $350 or less. We would be using it to watch movies, some TV, and project football games outside for cook-outs, etc. Does anyone have any particular projectors that they have experience with that can do these things? My main concern is getting the clearest, biggest picture for the price. Sound means nothing to me because we will be using a surround system.