Ok... since the shed is detached, you will need to install sub-panel in the shed with a main breaker. A 40 amp rated circuit should be fine for what you're doing, but I always recommend going up at least one size at the very least - it's very rare that a homeowner doensn't end up adding at least a couple of things that he/she never thought they would within 6 months of completing a project like this. But you are certainly free to choose here.
You could run #10 THHN and put it on a 40 amp double breaker breaker in the supply panel (in your house), and connect it to your main breaker in the shed panel (but I recommend at least a 50A breaker with #8 THHN, 3 #8's for two hots and the neutral and 1 #10 for the ground) Then you'll install individual breakers in the shed panel (20A single poles) to supply your receptacle and lighting loads. You will need to run THHN in conduit
or UF direct burial cable if you don't want to run conduit.
You will also need to drive two ground rods outside the building on the other side of the wall behind the panel in your shed. You will then need to connect them with a #8 bare copper ground wire with one continuous run to the ground bar in the panel to properly ground things.
On a side note, it doesn't really matter what size the main breaker is in your shed panel since the conductors are already protected by the 40 or 50 breaker supplying them. This purpose of this breaker is only to serve as a means of disconnect. So if you can only find a 60 amp breaker panel for instance, that will be fine.
I know this is probably a lot more than you were expecting, but it's code, and for good reason. Let me know if you have any additional questions. And good luck!