Continue with other types. Then if you want to have a turret shoot at only the ships in frigate class then you just set target priorities to frigate. It will ignore all other types. You can also change the group for a specific ship. This has never been tested but theoretically you could have a target priority group with nothing in it by default and assign a ship to it in mission. I do not know if this would work though.
Ahm, umm, there doesn't seem to be a SEXP for assigning a ship to a target priority group, is there?
I wrote a sexp that did what you want probably years ago now but no one cared and it never got committed.
Heck, that sure would make things a whole lot easier. Especially now that there are quite some mods that have non-beam anti-cap weapons and therefore can't nicely script their battles like fire-beam can. Do you happen to have the code lying around somewhere? People care now

Have you tried level 1 TAGging (choose the type of tagging via SEXP)? From what I could experience, it works without marking tagged ships with yellow brackets.
It is tagged level 1, but shows up as yellow. Changing the it to tag level 3, the hostile destroyer shows up red, without even needing the change-IFF-colour. So this is a step in the right direction.
Edit: However, the turrets are simply not firing now. Those that aren't slaved to the turret-tagged-specific work just fine, so it's got to be something in the SEXPs.