Pretty well all hosts use FTP, with the exception of a few tacky pop-up-ridden free hosts, who don’t seem to think their users are intelligent enough to cope with it. FTP is the standard way of uploading files anywhere.
And it’s not complicated - just go to a shareware site and download a FTP program, like Transmit if you’re on a Mac or Cute FTP if you’re on Windows. You can learn how to use most of them in about 30 seconds - they’re really quite simple. And a lot faster than those horrible upload forms at GeoCities et al.