The only thing a webcam needs is to be capable for 320x240 @30 FPS. Just about any webcam made this millennium can do that.
There really is no difference or advantage to getting a higher end webcam, or major difference between most common reputable webcams, as far as their function with LASR. The closest thing we have to a recommended webcam is the the Logitech C270, the only regular webcam offered in our online shop here.
We would generally steer folks away from the el-cheapo no-name webcams that you can find on the internet, simply because of poor build quality. They will usually work with LASR just fine, but they'll also break a lot and just be a general pain.