What type of cable should I bury for a small utility shed?
Why bury a cable when you can be future-proof?

The primary issue with direct buried cables is that you have to dig them up in order to upgrade them, a costly proposition.  Hence, it's a far better choice to spend the money to lay a couple of fat PVC conduits now and then pull wires through them, than to have to dig things up 5 years down the road because you want to turn your shed into a shop, park a RV there, or what-have-you, and you need more power for that than the original cable could provide.

Hence, instead of dumping some UF in a trench and calling it good, I would put in two PVC conduits, a 1.5" or 2" for mains wiring and a 1" for low-voltage wiring (such as telephone, CATV, or networking), both buried about 21-22" deep (to provide the Code-required 18" of topcover), and using prefabricated sweeps for the bends up at the ends of the run.  This way, you can run 4 10AWG THHNs (2 blacks or black+red, white, and green) for power to the shed for now, with a 100A or 125A, 24 or 30 space, main breaker subpanel at the shed to provide a disconnecting means and room for future expansion, and not ever have to worry about digging up wire and replacing it.

Note that if you go this route, you'll also need to run some 6AWG bare copper wire from the panel to two 8' ground rods, spaced 8' apart, in order to ground the shed properly; this is in addition to having a ground wire in the conduit going back to the main panel.  Don't forget to make sure that the bonding screw or strap has been removed from the subpanel, and that the ground and neutral in the subpanel are landed on separate bars, by the way!

Also, you may need expansion fittings on the stub-ups of conduit to take up relative motion between the buried conduit run and the buildings, say due to frost heaving or seismic activity.  Check with your AHJ for details.  Last but not least, leaving a pull string in the spare conduit is a good idea so that wires can be easily pulled through it in the future.