It depends on the reaction conditions. We do most of our precipitation polymerisations (with or without surfactant) at about 80°C. In this case e have good results with potassium peroxodisulfate or ammonium peroxodisulfate.

This works for acrylamides and also for styrene.

Need not to use couple of materials. You can use only Sod. Persulfate, its a cheep material.