For AP Physics C level, I am having trouble on deciding whether to use Ampere's Law or use Biot-Savart. Are there any hints/tricks for deciding what to use? For example, in solenoids i heard it's easiest to use Ampere's Law
If the system under consideration has high degrees of symmetry (e.g. spherical or cylindrical symmetry) then use Ampere's law. Biot-Savart is a brute force method that you only want to use when you have no symmetry arguments at your disposal. At the level of AP Physics C it will be obvious from the problem whether or not a system has high degrees of symmetry so as to allow for an elegant solution through Ampere's law.