frontal/melvin
back wedgie
bondage/ jock lock
atomic
ripping
all around
squeaky clean
hanging
dangling
bouncing/bungee
messy
permanent
You can also switch up location and underwear type, but I think the ones listed above are the main *technique* variations.
Am I missing any? To the second question, I like dangling wedgies, permanent wedgies (usually overnight), and slow squeaky clean wedgies. There's a particular friction that only certain wedgies give, and if you like it, usually the stretchier the fabric the better.