How large should my /home partition be, and which filesystem is best for Linux Mint?

You don’t have to create a separate /home partition at all. For a personal machine, using one large root partition with /home inside it is perfectly practical and avoids guessing how much space each partition will need. If the installer uses ext4 for the main partition, that’s a solid default.

For a typical personal computer, ext4 is the simple, dependable choice and is well supported by Mint. Format the partition during installation if it’s new or you’re replacing its contents. Allocate as much space as you reasonably can after setting aside the EFI, root, and swap areas, especially if you’ll store documents, photos, or games there. Btrfs offers features like snapshots and compression, but it generally needs more planning and isn’t necessary if your priority is low maintenance.

If this is a laptop and you may have sensitive files on it, consider full-disk encryption. Encrypting only /home can be simpler, but full-disk encryption protects more of the system, including temporary files and swap. Either way, keep important data backed up—partitioning by itself isn’t a backup.