Hi!
All of the options sound great, it depends on the use case:
1. If you plan to use these tags anywhere else than searching, then this could be useful.
2 and 3. The additional search tags is actually a custom field as well. I believe searching custom fields might give you a better performance. So, if you plan to use these keywords mostly for search purposes, then custom field/additional search tags is a better choice.
I hope this helps!