With a resolution no higher than 640x480, what is the frame rate I should expect for streaming? Are there any cameras in the 10-50 dollar range that will get me 20-25 FPS, possibly with some manual driver installation and so on?
The cheap (raw pixel) cameras will not give you a FPS even near the 20. They will only give around 2 to 9 FPS. This is mainly because the RPi will need to encode the frames before sending them, and that is a lot of data to encode.
With JPEG (those are mostly HD cams) encoded cameras you'll get a little better FPS rate (around 15 up to 20 FPS), because the encoding is done in the camera itself, the RPi only needs to send these frames without the need to encode.