You don't have to be a U.S. citizen or resident to form a corporation in the United States. You could do so yourself, but it might be easier to use an attorney. Take form Articles of Incorporation, send with a check to the Secretary of State in most states along with 3 name choices (in case yours is taken by the time you send the paperwork in). You need to nominate a registered agent for service of process, there are companies that will do this. Your initial address can be a Regus ($200 per month or so, and they will forward mail). You can get a tax id number over the telephone. Whether you can open a bank account depends on your relationship with the bank. Normally, this will be very, very difficult unless the bank is a branch of a bank where you already have a relationship. For now, just use paypal. You want to file an election as a Subchapter S corporation, at least initially, so you don't get taxed twice. LLC and C are apples and oranges, the first is a type of corporation, the second is the tax treatment. An LLC can be a C or an S. I should post the forms, it's not rocket science.
If you call Paypal with a US phone number and a foreign IP number, especially when the IP number is linked to a country with loose money laundering rules, you are going to have problems.
The key here is that $65,000 is not enough money for a U.S. investor visa. You shouldn't have been surprised at all. If the business idea is a good one, start outside the U.S., and then seek to establish a subsidiary in the U.S. With a proven track record, you'll get your visa, but by then, you won't want it because you won't want to pay U.S. taxes.
Take a look at the Craigslist message boards. You'll find all sorts of customer complaints about how Craigslist has been taken over by spam, in all sorts of areas, including the personals. Offer your site in those cities where the "overtaken by spam" complaints are the loudest and you'll provide a real alternative. There are lots of international destinations as well where you won't find Craigslist.