How do I decide whether to use Kirchhoff's Voltage Law or Kirchhoff's Current Law?

Whichever gives an easy set of equations. If you are doing resistor networks, count if there are more loops or more nodes. KVL if there are more loops, KCL if there are more nodes.

In more advanced circuits, like transistors, there is normally a very specific mode that lends itself to your problem space.

Do you want to solve for currents first, or voltages? Certainly once you have all the currents you can work out the voltages, and vice versa, but sometimes you're really after one or the other.

If you apply KVL, you end up getting currents first. This is because, to write the voltage drops around the loops, you use ohms law with the loop current, which is your unknown. So you write a system of loop equations and the solution gives you currents.

Conversely, with KCL, you can write the expressions for current into a node using ohms law to find the current contribution of a component in terms of the voltage differences between the node in question and the other node the component is attached to. Solve this system and you arrive at voltages.