Ideally, you'd pattern your gun/load/choke combinations & base your selection accordingly. This takes time, knowhow, & some money.
If you don't plan to do that, then I'd recommend these starting points. You can start there, & if you do enough hunting & get enough shot opportunities, see what kills best for you & dial things in from there.
These are based on my personal preference to be able to ethically take a 35-45 yard shot (assuming it's not a straight-away) because I can often make that shot & have a dog that will recover the bird.
It's also based on the fact that I hunt w/ a flusher & would never have time, nor the wherewithal, to switch barrel selection.
It's also based on my preference, as well as the generally accepted best practice, of shooting bottom barrel first, which seems to be inline w/ your approach.
It's also based on my preference to choke 1 notch tighter with a 20 gauge than I would with a 16 or 12.
And finally, the million dollar answer....MOD bottom & FULL top. Go IC bottom & MOD top with steel (#3 shot; #2 if you can't find 3's; never #4; at least 1,450 fps), assuming your "new 20 gauge" was built in the last 20 years.
If you do plan to take the long shots, switch to 5's or even 4's. 6's aren't reliably sufficient for even a 30-yard straight-away, much less a longer shot.
If you don't plan to take shots over 35 yards, IC bottom; MOD top. 6's are fine. With steel, CYL bottom; IC top; (3's or 2's; 4's as a last resort).