Check fold is fine here but would barrel hearts

I think that's a missread because hearts don't do anything on this board @StratoMan

I actually like a barrel here aswell. We don't have a lot of showdown value with king high and still get him to fold some better hands. I expect our king to be good quite often aswell and I think we're getting enough folds here to profitabily barrel

I think your line is standard. Two overcards and a gutshot is plenty good enough for a c bet and give up. With a 9 giving you an open ender I don't think you need to be looking for more out of the situation on the turn.

I guess we could 2-barrel, although tbh I don't think it's that important. Probably x/f is fine.

I also think we can start out with x/c flop here, might even be my preferred line. (Obviously with the intention to bluff later streets).