...if I go to Album, and launch the index.html file, in the browser it gives be a shell of the gallery, but only 20 images and the slideshow button doesn't work.
It's not that the files aren't where they're supposed to be. It's that a browser will refuse to open them locally. See this sticky thread:
https://jalbum.net/forum/ann.jspa?annID=213
I understand that FTP can work from jAlbum, but if I choose to use FileZilla, I'd like to know what files to upload.
You need to upload everything that's in the project's output directory -
Tools > Open Directories > Output directory.
But while you can certainly use FileZilla, I would strongly urge you to use the jAlbum uploader. The first time it uploads a finished album, it will take about the same length of time as FileZilla. But because the uploader uses a manifest file, if you make any changes to the album - adding a few images, selecting different skin options, changing styles, or changing the skin - the jAlbum uploader will be an order of magnitude (or more) faster. If you're just adding a few images to a large album, it can be hundreds of times faster.
The uploader also cleans up after changes. So, if you remove some images from the project, or if a change of settings or skins yields a different batch of resource files, the uploader automatically removes, from the server, the files that are no longer needed.