Wire size to run 200' to a shed
The capacity of the sub-panel isn't what's important, you could put in a 200 amp panel configured as a sub-panel and feed it with 14 ga wire on a 15 amp breaker.  Not a good idea at all, but it could be done. The wire size all depends upon the maximum load and distance. in your case #6 ga copper would provide you with about 50-55 amps, depending upon temp derating. Are you planning on a 240v sub-panel? If so, that would require 2 hots, a neutral and a ground. If only 120, it would need 1 hot, 1 neutral and a ground. Running large copper that far would be expensive, you might consider aluminum #4gauge for that distance.  Don't forget the &quot;goop&quot; (NOALOX) compound if you go AL.   You could get by with smaller wires, but like I said, it's all about the maximum load and distance. There's tons of info here at SE on installing sub-panels. I suggest you do a search and you'll be inundated with answers!
EDIT: In reviewing my answer I find it somewhat incomplete, so here goes with the EDIT:  The panel must be rated for AT LEAST the maximum power supplied to it. There is nothing wrong with installing a sub-panel with a capacity LARGER than the supply to it. That is commonly done.   I have a 200 amp panel in my shop fed by a 100 amp breaker.  I did that just so I'd have enough breaker spaces for my tools.
For us to better help you, add up all the loads you can think of that might be running at the same time. Going big on sub-panels isn't very expensive...going big on wire (esp. copper) on a long run can really run up the $$$, so a reasonable assessment of the loads is important.   So get back to us with the info for perhaps better advice.