Q: Is Minion still the recommended way to install AddOns?
Yes, very much so, it also will update existing addons.
Q: Does my ESOUI account show which addons I had installed previously?
If you've marked them as favorite then, yes.
Your last question is up to you, I have backups and have used them in the past.
Sometimes some old addons have stopped development, so you'd need to check which ones are current.
Hope this helps you