As an owner of all 3 minatos, it largely depends on a ton of factors. I am fairly high powered and have a decently stack pos1 int, so I usually run edo minato because with his undodgeable mystery (and someone who steals chakra) makes all those 6 path narutos cry. If I was not as high powered, I would probably go for Hokage Minato because of the resistance buff and if you have a shisui or a Konan [Angel of God], there's your tags for the enhanced mystery. I definitely had fun doing 3 minato mysteries in a row using wind main dance of inputus. The kunai passive is always going to hit so he stacks more reliably than the other minatos. Minato [Jonin] is both the weakest and the cheapest (so theres one good thing about him). He needs his bond mystery to be useable and is good when paired with a 5kage madara and a susanoo kakashi.

Problem is, like most things in the game, who to go for solely relies on what ninjas you have, what your playstyle is, what your power is, and what ninjas you typically go up against. I tend to go up against 6 path narutos and temporary immunity ninjas so my main team is usually edo minato and 5 kage madara with someone else mixed in (just got edo hashirama so its been him).

When you ask for people on the forum you're gonna get a lot of different opinions. That's just how this game works. When I was 100k-150k, I exclusively used hk Minato, shisui, wind main, and kurenai skill break