Getting a bank account for it is way more tricky. First of all, you'll need a EIN for your LLC, which you can get with your own SSN or ITIN only. Since you're not a resident, you're not eligible for SSN, and getting ITIN is a little bit of "catch-22" problem.
And even if you'll get ITIN and, respectively, EIN, you might have hard times opening a bank account. I personally was able to do that by e-mail/mail, but I was introduced to financial specialist by a friend of mine.
The specialist gives you an EIN over the phone. They then snail mail you a hardcopy in about a week.
From: http://www.irs.gov/businesses/small/article/0,,id=97860,00.h...
also some incorporation services do offer mail services on top of their "registered agent" service; although it is not that cheap and not that competitive, I guess
While I would probably agree with the advice given here about contacting a lawyer, you could start with BizFilings.com's 800#, and see if they can give you some good advice for free first. (I've used them in the past, and while I had a few minor complaints, they do a generally decent job for little money. In any case, they won't charge you anywhere near what a lawyer would.)
HTH
Officially with the LLC you will also have to submit taxes each year. LLC Taxes in the US are not low and are complex.
Other processors include Quickbook merchant account Costco Nova Networks Beanstream, PSiGate or InternetSecure. Chase Paymentech These are available from Canada - but most countries have clearing companies. Panama, Costa Rica etc with much better tax advantages then having a US Account.
They'll be able to handle the whole process for you, all you'll probably need to do is have a few signatures witnessed in your country of origin.