Yup Zebra is a type, I think it's more just different colorations though but I'm not terribly certain about that.
I know our Petco and Petsmart don't have Nerites but they might at yours. If not and you have a credit card or your parents do, you could order some offline. If you live in the US you could order from here: http://www.bobstropicalplants.com/shop/en/16-snails
I've used them for my Mini Yellow Rabbit snails and they came in great condition and they're very good on pricing as well!
It's also a hit or miss when it comes to Betta health with the bigger chain stores. Sometimes they will look really good but others they might be really bad looking. But if you find one that you like but it looks like it might need some fixing up first, you could always bring it home and ask the forum for what you can do to make him healthy again. Most Betta's will be much happier with warmer water and clean water and will get healthier that way but some might need a little extra care.
I assume you know about water changes and stuff like that? Also, if I remember correct, did you say you were cycling your tank before getting the Betta?
And no worries! Getting a new set up and fish is always cause to be excited for!