One thing I instantly want when reading your site is a gift :) -- you say "try it out" but I think it would be pretty magical if you'd just send me one if I type my address, or something like that. Obviously you'd want some way to prevent abuse.
Second thing I want when reading the site is to see the pricing on the homepage. I'm not in the business and have no idea how much these gifts are going to cost, so an approximate range (or, even better, github style "plans" showing various gifts and how much they would cost) would go a long way towards getting my email address.
Lastly, you could probably get away with an insanely simple "api" for your mvp that just let the person upload a CSV of addresses, and then dumped them onto a stripe checkout. You could build that in a day and (I'd guess) go pretty far.