Don't use the 'block of wood and a hammer' method of removing a nut. That splits out the fretboard. I've seen people knock the end of their Fender fretboard off when following a Gibson-style nut replacement video.
You can clamp saw bumpers to the neck against the nut sides so you can't slip off -- kind of like the kiddie bowling bumpers.
Get the wire $5 files set. Only buy the other nut file sets if you are going to do several guitars a day/week every day/week into the future. The wire files are slower to shape the slots and thus less risk of screw ups because you have time to correct an issue. Pro nut files will take a deep bite and gouge out the nut really fast.
Trick with nuts: make sure the bottom of the nut slot falls away faster than the string from the nut to the tuner peg, the slot highest point is at the fretboard side. Fret the 3rd fret and the gap at the first fret should be 1-2 pieces of photocopy paper gap. Bigger gap than that and you'll have cowboy chords out of tune when you play the guitar.