Screen for a basement setup with white walls?

A $25 gallon of dark flat paint.

Paint or treat the walls, ceiling, and floor 5ft out from the screen at the very least.
Then see how your current screen looks. Fixing the room will do a much better job of fixing your contrast and be far less expensive.

Although it is not essential to go with a very dark wall color, any color darker than white will be less reflective .. you have a good basic environment in a basement with no windows .. so, seriously consider darkening the walls .. as well as the ceiling and dark carpet ..

Otherwise, no matter the screen, you will be dealing with light reflection during your viewing times, which you will find to be unacceptable very quickly .. better to deal with it while in the building phase ..

As far as screens go, you did not mention a size .. however, with your budget, I'd recommend a Carada .. with a Brilliant White screen surface ..