Villain appears to be a regular and capable of postflop aggression

I have been reading a lot on balancing your c-betting ranges (particularly in 3-bet pots) recently and have trying to apply some of the concepts in certain spots. This is a low stakes hand so I'm not ostensibly concerned with perfectly balancing my ranges but rather looking to mix it up when the situation calls for it. The hand itself may not be that interesting but while it was playing out, I started to think how I would be playing other holdings on this board.

The flop is clearly not good for my range so I start with a check as I feel I would have to do the same with a lot of my highcards. First question I have is how relevant the fact that I have a redraw to a full house is. What if I had a dry overpair, set or some sort of weakish drawing hand (say JJT8 with a backdoor flush draw)? Which hands would you bet/call, bet/fold and check/call? Is there any need to have a check/raising range in this spot? I'm really interested how a well-balanced range would look like here (for example if villian was super-tough).

Please also comment on my turn play.

Thanks!