I never really understood the logic of stocking up on diapers.
First off, from my own experience, I have never seen a price change/great deal on diapers that didn't kind of pop up fairly periodically, negating any benefit from buying a bunch at once.
Second, you never know how long your kid will be in any particular size. So you might need to keep buying one size and then end up with a half pack of another because your kid then grew quickly past that size. (Friend gave me a whole pack of fours recently because of this.)
Third, kids have different sensitivities. I tried clothe diapering but DD always got a rash from it (when it wasn't leaking when she was too small.) She's had no problems with any store brand or name brand diaper (incl. Walmart, Target, Huggies, & Pampers) but other kids I know have a sensitivity to one brand or another. You buy a bunch and your kid is allergic, now what?
I'd just stock up on the newborn size and size one and play it by ear. There's no diaper shortage and I highly recommend using Diapers.com so you can even order online & get them in a day or two without leaving the house. (Slightly more expensive than the store brands (target etc.) but they accept coupons and often have discounts and promos that make them just as cheap and without the hassle. So no need to stock up.