I too recommend the Remington STS or Gun Club hulls. Often they're cheap and even plentiful.
Winchester literally wore out their ammo-making equipment for making AA-type hulls! Which is why they went to the newer inferior multi-piece "AA-hull" they now offer.
Remington offers a better hulls nowadays, when for decades they struggled to keep up with tinnchester!
BTW, you can use data from a [shotshell] reloading manual rather from the poor loads Lee probably lists in those presses/kits. Also keep your CF powder scales handy to verify powder amounts you use in whatever 20ga load that you choose.