Again, none of it is that "hard" (just can be intricate and complicated to get correct at first), just beware there are a lot of details to work out. IP also gets a little sticky if the co-founder lives in a place a little more lax about IP. Taxes even for the co-founder in his home country can be complicated cause the corporation will likely be required to register in his home country as well since the company would be employing him there. Check out the thread on international remote employees https://news.ycombinator.com/item?id=21841540. Since he would be a partial owner of the corporation you can't use the contractor method to avoid taxes like most companies do.
Talk to an attorney and a tax accountant/attorney. That way you understand it all, won't cost more than a few hundred dollars to save you a ton of money if you move forward.
Anyone can set up a company in the US, I'm referring to standard Delaware C-Corp. With or without a visa. With no visa (or with visa that's tied to another job) I highly recommend avoid standard documents that assume cofounder=employee.
Note that no visa = s/he can't receive money in the us, nor live in the us. You can pay a foreign person/entity, of course.
Moreover, with 51%+ in ownership from non-US (bare in mind this may change if you get VC funding, so likely doesn't apply to your case), the company is eligible for E2 visas which means the founders/top mgmt can get E2 visas, which is much simpler/less random than H1B.
But if the cofounder doesn't need to come to the US (often) then it's totally fine to not have a US visa. Hope this helps, best of luck.