I think you have to be really clear about your intentions before the flop is going to hit.. this is an easy call PF given the pot odds, but what do you want to hit and what do you want to bet on?

If you say, okay, I'm going to see if I can hit a straight draw or 2 pair with this hand before I commit money to the pot, then you go with that gameplan.. if you don't want to bet out when you hit a weak TP, then that's reasonable.

There's no rule on betting out when a J or Q high flop comes, I think people take different approaches here (leading out or checking to see your opponents strength first).. since you said he always min-raises, then I wouldn't be so quick to put him on a high pair, and i'd probably bet out here, then shut it down if he shows more strength..