Since you aren't looking to do any heavy pressure against the box, almost any Weldon brand acrylic cement will work. Remember that acrylic is plastic, so the glues work like model glue (if you ever built them as a kid). It melts the two edges and when you press them together, they basically merge into one.
Weldon 3 (I think I have this right, its been a while) is thin stuff, the higher the #, the thicker it is. If you are doing really clean straight cuts, go for a thin type, like weldon 3. If you are combining fairly rough (unsanded/buffed) edges, then use a higher # to get a good seal.
use only in a well ventilated area!!
Wade