Chokes in the 560- 570 range work best for turkey. In heavier than lead loads teh Federal HW #7 and H-13 in #7 are my top choices.
For goose,etc. try an improved cylinder or modified choke and Kent Fast Steel in #2, BB, . The 20 gauge is very capable of taking all feathered species, deer and bear, when shooting the appropriate loads, and ranges.
For slugs try Remington Accu Tip in rifled barrels and Federal Tru Balls 2 3/4" in smooth bores using an improved cylinder.
A 20 gauge has as much power as a 12 gauge given the same velocities and shot. The 20 may carry a smaller load but the shot string is shorter than the 12, assuming the same length shell is used.
More than anything, shooter safety first, shoot to know what your patterns and capabilities are at certain distances, stay within those limits, and know your target before ever pulling the trigger because you can never take back a shot.