My daughter is 5'0" and weighs about 110 pounds. She competed on her high school shotgun team. At practice they would shoot about 100 to 150 shells a session. At tournaments it would be more around 250.
I started her off on a 20 gauge, but within about 2 weeks, she switched to a 12 gauge. The first year she mostly shot a Browning and a Beretta, both gas operated. The 2nd year she moved to a Beretta over and under shotgun in 12 gauge.
Fit is important. Remember for skeet and trap, you are shooting light loads which don't recoil much. Also, a 20 gauge does not necessarily recoil less, because most of the 20 gauge guns are lighter. My daughter says she can't tell much difference between 12 and 20 gauge recoil.
I do think you are at a disadvantage shooting something other than 12 gauge if everyone you compete with is on a 12 gauge.