Online Canadian Business dealing in USA
You don't necessarily have to open an LLC in Vermont, but if you plan on doing business in the US I would recommend registering an LLC in one of the "incorporation friendly states" (such as Delaware or Wyoming). If you will establish real physical presence in one of the states such as Vermont you will be able to register a "foreign entity" of your LLC in that state. Delaware is attractive for retailers or those buying from wholesalers because it has no sales tax.
As for your company's bank account, I suppose if you are using a Paypal account and it's serving your business needs, then no it would not be absolutely necessary to have one. Keep in mind though, having a company bank account could help you establish business credit, which by itself would be a good reason to open one (and you can pretty much open a bank account in any state).
I hope you were able to find this answer helpful.