No big rules here, it's mostly a question of aesthetic and to avoid stretching the forum layout too much.
Avatars should not be bigger than 150*200, any size below is totally okay or even not at all, although it's always nice to put a picture on your nickname.
As for signatures you can either put text or pictures (or both) as long as it's not too big.
The best size to give you an idea is 540 to 600 wide and not more than 150 height.
Of course your images should remain SFW since everyone is going to see it without warning and overall, respect the rules of the Forum. Avoid flashing if you use gif for epilepsy prevention and straining colors/effects for the more sensitive eyes.