Looking for an inexpensive but bright and clear projector for bedroom.

Hello all! My wife and I are looking for recommendations for a budget setup for watching movies in bed, and we live in the northeast US. We have a projector screen that pulls down from the ceiling that is about 96" diagonal, and a high shelf about 10.5' away that would be perfect, over the head of the bed, but we could mount also mount a shorter-throw one on the ceiling if need be. We would be using a Roku stick for it, so it does not need to be smart, and while built-in speakers would be preferred, we could also put a bluetooth speaker behind it if it has the capability. We really just want to use it to watch movies farther away from the kids' room so we don't wake them up, and we'd like to spend around $300 or less if possible.