nylon would probably be too floppy. As well as being a more advanced filament to print properly.
pla or petg would be absolutely fine.

loads of free cad programs - I use openscad, which has a different approach. Good if - like me - you can't draw :-)
yeah no end of slic3rs around. Most are free. Depending on your printer, I'd say simplify3d is worth buying. But not a strict necessity.

check out thingiverse for existing files :-)