I never had to tape up until a recent six day gig with six sets per day. If/when you need to tape, so be it no big deal.
I used medical tape. Climber's tape supposedly works better, sticks better as some who've used medical tape said it didn't stick well enough. I didn't have time to get climber's tape and just raided the medicine/first-aid cabinet. It stuck well enough, but it's not humid here at the moment.
It was narrow 1/2" tape so I wrapped from the tip to the first knuckle so the overlap wouldn't catch on the string and peel itself off. For the same reason, I started and finished the wrap on the back of the finger. Once wrapped it lasted me all day and was easy to remove at day's end.
Unfortunately, it was the tail end of a roll. So I bought a new roll at the chemist's (drugstore) which was 1" and thus no need to overlap. However, not all tape is equal, even if it's the same kind of tape. The new stuff was a different brand and not as good. After 2-3 sets I had to re-tape.
I had blisters on both my pointer and index finger. I lanced them and kept taping for the remainder of the gig to give the popped blisters a chance to form into calluses.
I'll be picking up another roll of the brand of tape I first used and throw that roll in my gig bag if/when I need to tape again.
Hope you find what's right/works for you.