Yes you would be able to a 3rd party FTP Client with any web host. Or at least it would be really strange if you couldn't.
What I like about FTP Clients is that I can upload lots of files quickly and easily. Also they help manage logins and passwords for multiple sites that we you don't have to try to keep track of them yourself. This might not be an issue for you if you'll only have one site.
I know that publishing files from your HTML editor is usually pretty easy. You could definitely start out with just the integrated ftp in your HTML editor and whatever file upload page your web host provides. Then if you feel that you need more control more ease of use you could try out an FTP client.
YW for whatever light I manage to shed on the topic.