I can’t comment on the MySQL version but what you should verify before upgrading is that the appropriate PHP version is available for your Ubuntu installation.
When you update the first step is to put NC into maintenance mode => 0 active users.
Personally I recommend the cli updater. It outputs all error messages (if something bad happens).
You cannot skip major releases. Please re-run the upgrade until you have reached the highest available (or applicable) release.
I once had a really strange issue where web update would fail but didn’t give me any clue why. Only cli updater printed additional information that helped me identify the root cause of the failed update.
If you feel more comfortable using web updater - try it. If for any reason you run into an issue and web updater doesn’t provide any hints but just throws a generic error, switch to cli.
I’ve linked the official documentation above. If you’re lucky and don’t run into any issues you will hit the update button in admin menu 6 times and then you’re on the latest version.