As others have said, FTP shouldn't be a problem. My daughter used FrontPage to build a website for her work, and had all sorts of problems when the site grew and they changed provider. That's now sorted, and she uses FileZilla (one of the best FTP clients) to upload stuff to the site. She still uses FrontPage (but I'm sure she'll be cured soon).
If you are working on the site, I would recommend you download everything that's there now (the .php stuff and the database - probably MySQL or similar) before you make any changes. Burn it to a CD, check it's all there, and put it in a safe place. It's very easy to lose the lot with one wrong command, or a glitched piece of software. FTP will usually allow you to download it without too much difficulty. Some ISPs don't allow SQL download and will ask for £50 or so to make a CD or DVD that they post you. When choosing a new ISP, check that and don't choose one that does that!
Changing providers isn't a serious problem: your site will be "down" for anything up to two days while the DNS change filters through the Internet. You need the information to change the settings so that the new DNS appears against your web address, but that's not difficult. I did it, so it has to be easy!