Fastest: Incorporate in Delaware, cost $157+$20 overnight Fedex for a C-Corp, 24 hour turnaround, registered agent Incorp which is free for the first year and $99 after, done by fax. 10M shares at .00001 par value. $350~ a year franchise tax. Some banks may require a Certified Copy but my bank did not, which is an additional $50. Merchant accounts are pretty easy, just need to apply for one either at the bank or use a service like Stripe mentioned in other posts. All merchant rates are negotiable on the most part. I can start a new business within 72 Hours with merchant account and bank account, incorporated, full startup documents.
Foreign Corporations depend on if you have employees physically located in that state, certain states may differ. Most startups don't follow this rule, it's the wild west in the beginning.
Just make sure you keep good records and you get a decent accountant to make sure you don't get surprised come tax season. If your looking at the lowest tax rates on corporations, I believe Singapore and Hong Kong are great STABLE options, however they come with their own issues when it comes to accepting payments and also are much more costly to set up.
Get your corporation in order, get a merchant account and start making money. These questions are best left for accountants and even at that, not everyone will give you the same advice. Once you have revenue and you have an idea of what your working with, you can see if it's worth incorporating in another state/country.
PS: If your a startup with founders, check out Clerky.com. Very nice guys and will get your corporation done properly. Worry-free. I didn't use them because I was looking at maximum cost savings by doing it myself, but will invest in them later if we need to redo the paperwork or just flat out start a new company.