You may also need to take a few undergrad prereqs concurrently if you're changing fields (I had to brush up on some upper level chem and bio) at the same time and that can affect costs if your upper level degree is different than the field you start out in.
It is tougher to transfer in graduate schools, though many phD programs offer funding whereas Master's tend to be work (Employers will sometimes pay for you to take courses - this is likely very limited for an international student) or loan/self funded. As an international student, you would do well to look into scholarships and TAships. Work hours are often limited and TAships tend to pay better than most jobs as well as looking nice on a CV/resume.
I do suggest getting in touch with a professor or mentor when you choose a program. Being known to a professor can help you get in on tasty, tasty not-loan fundings since they often have a say in departmental funding. Be sure to know what they study and let them know you're interested.
The costs of a Master's or phD vary considerably by school and region (as do costs of living. Look at the cost of living in NYC vs say, somewhere in Austin, TX) as well as what program you're interested in. I would disagree that going straight to a phD is dumb. It's simply for some people, and not for others, that's all. And sometimes you can come out of it with a Master's if it doesn't work out in most cases.
However, I do believe that I should warn you that a phD in and of itself can be very limiting, should you choose to walk that road. Humanities phDs are not 'stupid'. They are simply harder to sell and you'll have to hustle a bit more. Be prepared to learn to sell your skills and make connections.
We might be able to help you more if you'd let us know what subjects you're interested in. I also advise you think long and hard on what you want to study, not just the cost. US programs are much longer and a good chunk of them are research focused. Most schools do want to help you attend, after all.