As Stinky says, sftp is the easiest way to handle things; this is a file transfer service that works a lot like ftp, but transfers over a Secure Shell connection, so you don't give away any passwords. If you get SSH running, then sftp should be automatically included, and should work okay.
Using non-root FTP is possible, but you have to create a user account with a separate password. If you're uploading to the internal card (eg, /media/fat/games), the FAT filesystem there has no concept of security or permissions. As long as you grant R/W access in the ftp daemon, you should be able to load stuff with no issues from any user account, and it will all run fine from the main Mister menu. However, if you ever upgrade to a better filesystem (like by attaching an external USB device), you could run into permissions problems that you'd have to fix from the command line, possibly by creating a new group and assigning permissions to that.
I can show how to create users if you need to, but I'd recommend using SFTP instead. It just solves everything all at once, and it will keep working in the future. There's a little bit of friction in getting your client set up, but once that's done, you can just keep using it no matter what you do with storage on your Mister.
edit: also note that Windows 10 and later have a text-mode sftp client built right into the OS.