If you have a plastics supply nearby, see if they have IPS Weld-on 3. It's a water thin, fast curing glue for plexi, but it works great on just about any plastic including styrene. You can get a quart for about $12 and that should last the average modeler a long time.
The only problem with superglues, is over time they can become brittle and break apart. A combination works great too. Use a little CA on each corner for a quick set and then use the Weld-on along the rest of the seam for a strong, chemical bond.
The plastic place will usually carry applicators too.