Remington Gun Club loads are fine.../ they're the less expensive target shell made my remington - where the Remington STS or Remington Nitro is the premium Target shell.
Remington makes all kinds of "game loads" ...and yes in general they're good shells.
In a 20ga...the standard load shell is 7/8 oz. In a 20ga - most shooters will shoot 7/8 oz of 8's or 9's ...for clay targets. Very few shooters will shoot 7 1/2's in a 20ga ....but no reason why you can't either. The 7 1/2's will carry their momentum a little further out ...to 40+ yds.../ but for Skeet or Trap 9's or 8's are plenty.
You will find a number of shells for the 20ga - in 1 oz loads as well.../ and you should see some with 3/4 oz of shot as well...depends on what you want.
You pick the shell...and the shot size - to fit your needs. Every game bird is a little different ( some tougher to kill than others - so you need bigger shot - not more, just bigger) ...and the expected kill range is different - early season pheasants over a pointer, is different from late season where shots are longer.../ so its hard to say if you should buy 6's or 4's.../ or both...
Most clay target ranges - will not let you shoot any pellets bigger than 7 1/2's...( they want to control the shot fall zone ) ....so no 6's, etc on a Skeet, Trap or sporting clays field.
A single shot may be fine....although I'd probably recommend a pump gun over a single shot for more versatility - especially hunting / because you don't want to cripple live birds - and you might need a quick follow up shot.