Regular cycle, hottest water, unless a particular item is delicate enough to be ripped by the agitator (and you don't have a mesh bag to put it in). Most "delicate" or other non-reg cycles use colder water and less agitation, probably a slower spin dry at the end. No need for this with MF towels, which are not delicate, so give them the good stuff. Like I said, many FL washers have a "sani" cycle that is good for MF towels.
Distilled white vinegar is a good call. I use DWV in the rinse for everything, including MF towels.
Second rinse is just water, BTW -- first rinse is where the DWV comes in.