Go here for a calculator and fill in your parameters.
https://www.southwire.com/support/vo...calculator.htm
Direct burial is "the norm", but if allowed I would use the gray pvc conduit buried.
Then pull individual wires (not the all-in-one romex).
Reason being, if one wire develops a problem you can pull out and fix or replace just that one wire.
I would also try to run 220 if at all possible then use 110 from the sub panel in the shed. When you can get a super deal on some sort of 220 machine, you will kick yourself for not running 220.