#6 UF should be more than adequate for your current needs, assuming you aren't running any welders
or anything of that sort. And by that I mean, you would fine running electric drills, saws, etc. #6 UF would give you a 55 amp rated circuit. Conduit
and THHN is the always the best way to go in my opinion, especially when you get up to 100' or more simply because if you ever have any problems or want to upgrade, the conduit is already there, all you have to do is pull new wire. With that in mind, I also recommend running the next size conduit to allow room for larger conductors in the event that you do decide to upgrade later on. This is all preference of course, you are not required to run THHN by any means. #6 THHN would give you a 65 amp rated circuit, and #4 would give you an 85 amp rated circuit. If you choose to run #6 THHN, you would need a minimum 3/4" SCH 40 conduit, but 1" would allow you to install #4 THHN. Also want to mention that you only need a #10 THHN ground for a 60 amp or smaller circuit, and a #8 THHN ground for a 100 amp or smaller circuit.
You'll also want to make sure you use a sub-panel with a main breaker in it. It doesn't matter what size the main breaker is as long as it at least the same size as the breaker supplying the panel or large. This breakers sole purpose is to act as a means of disconnect, not over current protection. The wire is protected from the breaker you install in your 200 amp main panel that is supplying this circuit. Be sure to drive TWO ground rods outside the shed and connect them with one continuous run of #8 copper to the ground bar in the sub panel. Also make sure you have separate ground and neutral bars. You may have to buy the ground bar separately as some brands of sub panels only come with a neutral bar.
Let me know if you have any additional questions or concerns.