Should I get both top and bottom permanent retainers or just bottom?

What you are referring to is "fixed" retainers. They are not necessarily permanent as they can break, come loose, etc. There are a lot of factors to consider when choosing to get fixed retainers, including how the initial alignment of the teeth was, how is oral hygiene, condition of gums and bone, etc. But assuming that you have discussed all this with your orthodontist, generally the lower front teeth are good candidates for the fixed retainer. Upper fixed retainers may not be an option in some people due to the way the lower teeth hit the inside of the upper front teeth. If you do get a fixed retainer, it will still help to have the clear retainers made over the fixed retainer/s.

I always encourage patients to get both top and bottom permanent retainers if possible, in addition to the clear removable ones. Over time you will become lax in wearing the removable ones but the permanent ones are meant to be worn for life.