No mystery about what's in a finished album. From within jAlbum, open the project, then choose
Tools, Open directories, Output directory. Everything you see there needs to be uploaded to your server, and nothing else.
I use FileZilla for my own site, but use the jAlbum uploader for stuff on jalbum.net. I just like the visual feedback and degree of control that FileZilla gives me. There's no need to puzzle over what to upload. FileZilla has a built-in routine for uploading only new or changed files - it quickly hops, skips, and jumps over the others. So, you can just mark all of the output files and folders in the PC side, and tell FileZilla to do its bit. Much safer than guessing about which root-level files and folders also need to be uploaded, even if you've made changes only in one folder.
In FileZilla, choose
Edit, Settings. Then go to
Transfers, File exists action and for
Uploads, choose
Overwrite file if source file newer.
Last but not least, when you get close to the end of your agreement on GoDaddy,
leave. Not a great web host. You can't go wrong with any of the top few hosts on this review site:
https://www.reviewhell.com/. I host all my stuff at MDDHosting, and have been very happy with them.
It wouldn't hurt to move your domain registration when it comes up for renewal, too. Don't wait until the last minute, in case there's a snag. I recommend Namecheap.