I need 3 circuits in the shed. One 20 amp and two 15 amps. Should I run 30 amps of 220 into a sub panel and split there or 2 runs of 30 amp 110?

110 and 220 do not exist anymore, it is 120 and 240. I would run a piece of #8/4, because of the distance, and a small subpanel. Subpanel install requirements have changed over the past few years, be sure to read up on them. You will need a grounding rod at the shed.

What are the circuits for?
If you really need three 120V circuits then a sub-panel is your only choice.
If you can get away with two 20A circuits then you can run one multi-wire circuit which is two circuits sharing a neutral. This is also an easier choice because no ground rods are necessary then either.