Let's say we are in the SB 23-ish BB deep. We minraise (say 70% with no limp-range to keep things simple and ranges wide) and and unknown villain calls. Let's consider the following flops (villain checks to us in all of them)

FLOP 1: KK2r

FLOP 2: 889 (two hearts)

On flop 1, it shouldn't be that complicated, should it? I'd tend towards a small c-bet (40% seems too big, probably 25-30% is best) with all kings, pocket pairs or deuces (for value). Qx looks definitely not a value-bet, but what about Ax? Does it make sense to bet some of those? I should also pick some bluffs to balance my range. Should I pick hands with no showdown value like 67o and alike despite now having much equity?

Flop 2 is slightly different because my range has a lot of semi-bluffs. I should definitely bet any 8, 9 or TT-AA, and also all my 8/9-out draws. I'd also pick a bigger bet size, but how much bigger would be correct? Should I also include gutshots and other easy-to-fold (when villain check-raises) bluffs?

What are your thought? How do you approach these spots?

On kk2r it's definitely viable to just minbet range.

889 gets more complicated, wouldn't be shocked if you could still profitably minbet range vs field but I definitely would prefer to mix in a decent number of checks as bb hits these boards pretty well. Still small sizing tho.

Thank you for your answer!

In case we wanted to have such ckecks in flop 2, what would you choose them to be? Maybe some Kx or Qx with no draws nor blockers?

Yeah most of my checks would probably be high-card oriented.