I've got the appropriate amount of light for my microscope ring light, but now I need to put it all in an enclosure of some sort.
If I don't have a custom board to solder these to, what are my best options for connecting these she mounting them into something?
If this is too vague, please let me know if I can clarify
It all depends on how fancy and compact you want it. Technically you could cut holes in cardboard, poke them through, then hot glue them in from the back.
I'd probably 3d print the ring with holes for the LEDs then hot glue the back side. Perf board is good to put a bunch of components close to each other to connect them. Since the LEDs need to be in a ring pattern, it seems like you'd end up cutting the perf board into small pieces just to attach it to a ring of some kind.