I second the recommendation on the book that Gresham mentioned above.
The easiest jellyfish to keep are Cassiopeia sp. They require a set-up/care similar to that of the corals we keep in the hobby, and do not need to be fed as often as many of the others (they have photosymbionts). Any hobbyist that can keep corals successfully could probably have luck with these with the right set-up.
Moons are probably the easiest planktonic jellies to keep. Because they need to be kept suspended in the water column they require a much different set-up than a coral system. People typically provide them with a kreisal, pseudokreisal, tumbler or similar set-up with just the right water flow to keep them suspended without tearing them up. Most people typically provide them with 55 degree water or so as mentioned. The basis of their diet is typically live brine shrimp nauplii, although most will offer other food such as black worms, blood worms, mysis, and krill. Alot of people have stopped feeding cyclops to jellies although certain people still do as part of the diet without any noticeable detrimental effects.
Beyond these two genera you will likely get into more difficult to keep jellies and much harder ones to acquire.