Materials for simple wall shelf

I want to build a simple wall shelf to hold a projector and probably a few other small things; no heavy weights.

I have some cheap 7" x 9" shelf brackets (just L-brackets) that I was thinking of screwing into 3 studs and getting some kind of 12" x 36" board to span the three brackets with a bit of excess on both ends.

First of all, is this a good plan? Are my brackets good enough for what I want to do/is there a better or simpler way to do this? This is a rental, so a few easily-patched screw holes are fine, but I can't do anything major or permanent.

And second, what type of material do I want to use for the shelf itself if I want to avoid bowing/sagging in the longer term?

Thanks for any help.