for the start... search, download and read AN47.pdf (High Speed Amplifier Techniques)
- Unterminated Pulse Generator AN47-7
- Poorly Terminated Line AN47-8
if you have more spare time, search for member like w2aew and jahonen etc and look out for precious gems in their posts. they are very sharp at the physics of this subject, also they have website and videos. above all... practice. trust me the gems are meaningless without practising it, you wont get it at the first sight. hope it helps.
edit: ei i forgot the real question... yes, for few tens MHz work and above you need BNC, coax, termination, pain and suffering...
Q: Does function gen also need some capacitance compensating like an oscilloscope?
A: depends on your connection, long coax needs compensation aka terminator at the end. Jim said, the best probe is no cable at all, so possibly no need terminator but... it depends.
Q: How do you guys connect your function gens to circuits?
A: coax cable and termination, some time direct to BNC connector on the board, alligator clips if the signal is slowish and again... it depends.
Q: Do you have some BNC -> crocodile clips adapters?
A: oh yes we have a lot, some by intention most by mistake, collected during a long span of time. variety of brands and mods
ei and for the last edit, an advice... also make sure you have a solid PSU, the best is non-faulty LA battery for low power circuit. whacky PSU is quite enough to get you into hair loss problem.