This is a great question and I'm looking forward to seeing others' responses.
For me, I rarely if ever bluff shove, I do sometimes value bet bluff if the board makes sense and I feel I'm against a villain that actually understands the board texture. I think it's futile to try to bluff against players who you feel do not understand the board and are only absolutely playing their own hand not considering your possibilities. My opinion on the matter is that way too many players bluff shove without understanding why (does the story they're telling make any sense and even if it does do their readers/viewers of said story understand it anyways?).
As for min raise bluffs, I think they often fall flat and fail because "it's only X amount more" villian may think to bluff catch you with their A high or low pair.
I think a value bet bluff against a villian that can find the fold button on a board that makes sense to do so on can be effective. I want to bet the least amount to get the job done, I also see little point in risking my entire stack (cash or tourney) to win a pot when the same fold can be achieved with a smaller value bet against certain villians. Plus, if I think villian has no fold button, I'll sometimes give up the pot, no point in getting check/shoved into oblivion (see my recent post on how I should have taken my own advice!) when the villian probably isn't going to fold and probably has me beat with a bingo hand or low pair.