I think the flop bet is fine. I'd check the turn on a dry flop and bet on a wet flop. I'm very happy if two bets go in postflop.

In this particular situation with some straights and thus some two pairs possible, I would probably c/c the turn. That really defines our hand but I wouldn't expect villain to know/exploit that. And then make a decision on the river, expecting him to often check it back.