The point is ....you can't shoot 6's ( or any pellet larger than 7 1/2's on most any Skeet, Trap or Sporting Clays ranges)....
But shooting 7 1/2's or 8's at clay targets ...is not a disadvantage, it will get you some time with the gun ...hopefully improve your wingshooting skills.../ .... its not about how many pellets are in the pattern...its about the fundamentals of executing a shot at a flying target...( and not getting in trouble with the range - for shooting a shell that they do not allow you to shoot ).
The gun you have with a Modified choke...will be fine for a game like Trap singles from the 16 yard line.
I'd suggest you go out to your local skeet or trap club....buy some 20ga shells from them ....and have some fun ...and not worry about what pellet size you might use for hunting yet - that will come later.
But put a few hundred shells thru the gun ...before you go to the next step / don't get ahead of yourself.