What kinds of gaps/tolerances should I use when designing pieces that fit together?
I use my clearance values according to my rule of thumb: 0.1mm - to fit with some force, 0.2mm - just fit edge to edge without force.

Examples:

1) 3mm metal cylinder to be pressed into plastic part needs 3mm+0.1mm*2=3.2mm diameter printed hole (clearance from two sides)

2) 3mm screw to fit into plastic part needs hole bigger than 3mm+0.2mm*2=3.4mm that is 3.5mm will be already good.

This is fully experimental but always worked for me on three different printers and both on PLA and ABS.