Most every prebuilt box I've seen, aside from also using brad nails, they use some kind of very hard plastic feeling glue. What kind is it or should I use?
Titebond 2 only. I've tried them all and Titebond 2 is the best. Titebond 1 and 3 are good too but Titebond 2 is what I always use. You'll notice all the guys that build lots of boxes use a Titebond glue.
I always use Tight bond 2 and a few Kreg joints. Always solid as a rock. Last time I did just glue and clamps on a sub box it blew apart in a week after sub broke in.