Powering shed (office) 200 feet away
Do some research on how to do a load calculation on a building, that should give you a good idea on what size service you need. Once you've got that, you can use tables and voltage drop calculations to determine wire size.

Here's an answer, that describes an easy way to calculate the load for lighting and general use receptacles. On top of that, you'll want to calculate the load for any additional items.  You mention an A/C unit. You'll want to check the nameplate on the unit, and add the A/C load requirements to your total load.  Do the same for any items that are larger than you'd plug into a typical wall socket.

This answer gives some good information about how to size the conductors, once you've determined what size service you'll need. This answer will show you how to calculate the voltage drop, so you can determine if you need to use larger wire or not.

If you can get your hands on a copy of the National Electrical Code, article 220 is a good place to start for information on doing load calculations.  NFPA offers free read-only access to the NEC, all you have to do is sign up for an account.