I would suggest a GoPro, but you can't zoom the Hero 3 that I have. Not really low cost either, but certainly waterproof. When it is in the water proof case, the sound cannot be heard from outside, so you might need an additional mic.
I would look for one with wifi like the Gopro, but with zoom and is water resistant rather than waterproof. That way it can catch the sound.
You can always mount a piece of glass in front of any camera and that means you can go very cheap.
You will need extra lighting. My enclosure has plenty of light for machining. Two bright spots on each side. Then I also hung a drop light inside and it was still a bit dark.
I corrected it some with editing, but you can't beat having the correct amount of light to start with.