I have an intro I created that I'd like to export and then re-use in other various Premiere projects (which obviously means I'd be re-exporting this intro), but I don't want to lose video/audio quality..
Could someone tell me the absolute best export settings for the initial export?
If there are graphic elements, I'd choose a 10 bit codec to preserve details. ProRes 422 is a good choice for preserving exports. If you do not have graphic elements, then ProRes LT is a good compromise on file size. GoPro Cineform also offers 10 bit codecs, that are popular choices, as well. I just don't use them.
Several options. You want an intraframe of medium to low compression ... which would be Cineform, ProRes, or DNxHD/R primarily. Say ProRes 422 would do fine, with that or the other two codecs you can go several generations without seeing any degradation.