The same factors that effect your own pops happiness effect conquered ones, they will be at a disadvantage no matter what for a few years as they integrate into your empire.
If you damaged the environment with bombardment, unrest will happen, if you damaged it too much, then significant deaths will occur. At a minimum, ground troops stationed in sufficient numbers will reduce unrest levels. They need protection like any other colony, and since it likely is a homeworld they might need a lot of it, or you can just let the ground troops keep order.
As to colonization, you may have to start it manually by placing a few on there, but after that the civilian shipping should take over in their own way. It has been a bit since I observed this myself though so there is a possibility I am incorrect.