I will second that you need ventilation, regardless of what you use. The solvents that you can use with acrylic paints can be irritating to the linings of your airways, too. Can you open a window?
I work in my basement, too; it's about 50'x 20' or so, and it's at the end of the HVAC system (there are registers to bring in air from the forced-air heating system), but I do have ground-level windows on three walls. I have no problem with Testor's tube glue or enamel paints, Plastruct's Bondene and Weldene, and various enamel paints, when sitting at the bench and working with those products at close range. But when I airbrush in the same space, I have to use active ventilation.
gregthec
...Can I use acrylic paint on polystyrene?
Yes, absolutely. I use acrylics (primarily Tamiya, Andrea, Vallejo, but also craft store brands) as well as enamels and lacquer-based paints, on styrene kits. I apply them by hand, or by spraying with rattlecans or the airbrush.
I recommend cleaning the kit parts first, with a bath of warm water and a couple drops of something to remove grease and de-molding agents. Some use dishwashing liquid. I started using the automotive de-greaser Super Clean a couple of years ago. It leaves the surface literally squeaky-clean, and you have a good surface for a primer to adhere to.
Then I would prime the pieces, before applying your finished colors.
Hope that all helps!
Best regards,
Brad