Backing up the drive:
If you can access the drive using LiveUSB or by removing the drive and plugging it into another machine, I would actually recommend against using a GUI backUp creator like Timeshift or DejaDup.
If your edition is 12.4 and you are moving to 16.3, that is quite a leap. Trying to solve Software from two editions back will be problematic. It really is personal files and data that gets priority for your needs. Even your home .config directory can be ignored since many of those configurations won't match the standards on 16.3 from 12.4
I would just go through the HOME directory and start with your desktop or documents folder and look through what you want to keep. If you want to keep everything, right click your ~/Documents directory and choose to Compress the file. You can compress it as tar.gz. Compression of a large directory can take a long time. But it would take just as long if not longer using a GUI backup tool - since compressing it is the first thing that it does, too. They usually then add their own markers or encrypt it...
Repeat this for Pictures, Videos, etc.
Make sure you reveal hidden files and look through your home non-hidden and hidden files. For example, since I use launchpad, I would save a copy of dput.cf from my home directory. You may have similar files. If not then, you are in the clear.
You may want to keep a copy of bash-history or wget-hsts.
You won't need to save copies of your bashrc or your xsession or .profile.