These situations will have different best actions for you depending on your opponent. Your opponents tendencies will help you decide whether to bet or check at first. But you don't want to be giving up too easily regardless of the opponent. Practice will help you get more comfortable in these spots.

Think it obviously depends alot on positions , board texture and opponents.
I think a good place to start is cbetting more vulnerable hands and cheking back the less ones. For example:
Co vs bb deep, u open 88 the bb defends and the board comes J23r, i like betting here more often than not cause u arent getting much xraised and hands like T9 that have decent equity against u arent able to continue. And u still get some value from Ahigh , some gutters ,3x etc...
Other example: u open KK utg , and btn flats. Board comes A72 r, here i think its a xback almost always since u dont have to protect at all, u are unlikely to get value from worst and if u think u are faced up against aggro villains that would turn probe and bomb river, just xback some Weak Ax and some AA ocasioanally.
Hope it helped some, but i think there tons of different aspects to each hand, especially in mtts that are difficult to create a fixed strategy.