Outbuilding branched from LOAD side of GFCI
10 ga copper would be quite adequate for a 20A feed if purchasing wire for the job. 12 ga would do for most purposes. 125 feet at 20a (or 16A continuous) is not that bad a run, particularly if you don't get hung up on the 3% guideline (not rule, unless Canada, I guess.) Given &quot;the work of digging the trench&quot; and the cost of conduit (once) for options to pull wire out and in if/when needs change, I will, as usual, advocate for conduit.
Bury the 6/2 UF if you want to &quot;because it's free&quot; and you're digging a trench (and junction box splice it to smaller conductors at the ends, a few feet of 10 or 12 ga won't bother the overall voltage drop at 20A) and put in empty conduit (or conduits) for &quot;whatever comes next.&quot; Or fill the conduit to run more than one of your 4 circuits out there. You can change the splice connections to 6Ga if you ever up this to a larger feed, but that wire will (practically) be limited to 120V - just think of it as a 120V circuit only, or two if you have 250 feet of it to make a double run as completely separate circuits.
Don't try to put the UF in conduit - it requires a huge conduit and is not practical (nor easy to get into the conduit.) Use THWN in conduit.