Having a set, i would only check the flop if:
- ..it was dry like 3⋄8♥J♣ My reasoning is there are not enough high cards and draws for someone to have hit something and following me.
There's no other case in my book for slowplaying a set. Slowplaying is overrated and a nice way to lose a whole street of value.
On a flop of
78T i'm suspicious of any
9X and a handful of other combinations and therefore i'm gonna bet every street.
It's better to bet straight away from the flop, most players think you can't have a set and bet it right away on the flop, so bet it.
In addition, many people just check/raise frequently and only on the flop, so don't waste a nice street of value, especially if you were the preflop raiser and just C-bet in their thought.
It's also depends on your opponents; check/raise on aggros, value bet or c-bet straight away against tight players.
If a 9♣ comes then it comes, you bet correctly anyway. This is where position becomes very important; you're going to witness how they react on Turn before you and gaining a free street (mostly) to the River, having around 25%-30% to improve to a full house after they check to you, which they do even with a straight, thinking you may bet again.