If you wash the model, using dish detergent and warm water, then rinse it thoroughly and allow it to air-dry, many paints will work just fine on styrene without need for a primer.
Some exceptions might be some varieties of craft paints, which are often meant for use on paper or other absorbent materials, and brush-applied lacquer-based paints, such as Floquil. The latter will stick to the plastic very well, because it will attack the surface of the plastic, often leaving a pebble-like surface. Airbrushing lacquer-based paints yields much better results, as the paint dries-to-the-touch almost instantly.
Most acrylic paints work well on styrene, and the better quality ones (my favourite was the former PollyScale paints) can yield great results when airbrushed or brushed on with a good quality brush.
I often primed unpainted or stripped models that were cast in black plastic using Floquil’s Grey Primer, as it provided a neutral colour onto which pretty-well any colour, including white, could be applied.
Another good reason to use primer is when you have a model which consists of many different-coloured parts, such as a black styene boxcar to which you’ve added grey doors, a brown roof, white placard boards, and brass grabirons.
Like the all-black boxcar, the primer will give you a uniformly neutral background onto which any colour can be applied, and when dry, will be uniform in appearance.
Nowadays, if I’m painting something cast in a colour other than white or light grey (or maybe cast in a colour similar to what I’m using to paint), I’ll give coat of grey primer, using either Tamiya’s rattle-can version or a similar grey from Alclad, which is airbrush ready.
Wayne