The question for you is what type of dumplings do you enjoy eating out? Is it the Northern Chinese kind with a chewy (sometimes thicker) skin? Or is it the Japanese gyoza with the see-through skin?
I think the ones called just dumpling skin is the thickest, Shanghai style skinnier, and gyoza skin the thinniest. For pot stickers, use the same skin as what you would use in steam/boiled dumplings. The yellow kind has egg (and yellow food color) in it, and those are strictly for wonton (HK style only) in my opinion. Even the Shanghai style wonton use white skins.
Har gow (shrimp dumpling) typically use a mix of wheat starch/tapioca mixed with boiling water; not sure if I’ve ever seen the dough sold separately. The shumai dough is hot water dough/regular dough/lye brushed dough, depending on what region we are talking about.
Cheung fun noodles (rolled up or cut into slices) can be found fresh or dried in Chinese store, but normally not used for dumplings. I’ve seen people making them at home with a steaming machine with several drawers, but I don’t eat enough of those to invest in a machine.
I’ve bought the gyoza wrappers occasionally when the craving hits - and this is from someone that grew up making dumplings with mom and grandmas every week. But the store wrappers honestly cannot hold a candle to homemade wrappers, and I really encourage you to give it a try. It’s really a frustrating experience making pleats and trying to press the seams together on a store bought wrapper, where as a homemade dough just meld right under your hands. It is a project on your own, but get some friends/family to delegate and put a silly show on the background, it could go very quickly!
