It's really easy to get good results with mainstream hobby products. Plus, for the most part, you are not going to have compatability problems that you may get with automotive or hardware store products that are not made specifically for plastic models. That doesn't mean you can't get good results with those products, but if you don't know what you are doing, you can screw things up fast, and irreversibly.
Testors, Poly Scale (now discontinued), Tamiya, Humbrol etc. all make a variety of enamel and acrylic model paints that are styrene safe. Testors, Tamiya, and Gunze also make some styrene safe lacquers.
I use an airbrush, but for large models, simple color schemes, or schemes that require masking, I often use spray cans. I prefer the Tamiya spray lacquers... they dry very quickly, go on very thin, and are extremely durable, especially the metallic colors. Put them down first, and then you can hand paint details on top of them with other types of paint.
For painting little details you can use enamel or acrylic paints. Perhaps what kind you get is based on the color you want? Some shades may only be available in one formula or the other. I don't like a lot of acrylic metallics either, so often I use an enamel for those colors.
For brush painting larger areas or the whole model, I find some paints work much better (or worse) than others. While I like Tamiya acrylic jar paints for some detail work, and airbrush use, they are not the best to brush paint large areas. They dry too quickly to level out smoothly, and although they are acrylic, they are still solvent based and subsequent coats will easily lift up the first coat of paint.
The old Poly Scale stuff brush paints very well. I have had reasonable success with SOME of the Testors Acryl acrylic paints too. Oddly one color may work great and the next will be thin, gloppy crap.
Humbrol enamels work very well. You have to THOROUGHLY mix the paints (i use an electric stirrer) and let the individual color coats dry overnight or a bit more, but they are durable and you can paint colors on top of each other without lifting or clumping.
Revell Germany and Tamiya enamel paints also brush paint very well, although they are not sold in the USA so you need to get those mail order.
Vallejo acrylic paints are excellent for brush painting. They offer a vast line of colors in several series like Model Color, Model Air (airbrush), Game Color (sort of like the Games WOrkshop line) and a Railway Color line. They do not stick to bare plastic though, so you need a primer.
I prime some kits and don't prime others. It may depend on how much puttying, sanding etc I do first, or what color the plastic is. If your model is in black plastic and you want to paint it yellow... you will NEVER cover the black with just translucent yellow paint. And, as mentioned, some paints (mostly acrylics) don't stick well to bare plastic. Generally I use Tamiya Fine White or Grey spray primer.
This original Aurora Hunchback was hand painted with Vallejo Acrylics. I did the whole figure in about 6 hours spread out over two or three days
I did paint this Polar Lights Hunchback with Tamiya acrylic paints, and it was a pain. So yeah you can do it, but is it worth the hassle?
Atlantis/Aurora's Zorro was done mostly with Tamiya spray cans. I used Flat Black, Satin Black, GLoss Black, and Tire Black. The details were painted with Vallejo Acrylics. The base was spray painted with Tamiya Desert Sand and detailed with Vallejo washes.
Monarch's Sinbad was hand painted pretty much entirely with Vallejo acrylics except for the stone head which was airbrushed with a discontinued Testors acrylic ship paint
KP's MiG-17 was hand painted with Poly Scale Acrylics
Airfix's Bismarck and Hood were done with Tamiya spray paints for the grey and red shades, and Humbrol enamels for the decks and a lot of detail painting.
Even complicated, multi color schemes can be done with spray cans like this 1/72 Chance Vought Vindicator. The model was spray painted white first, and all subsequent colors sprayed on top. Tamiya tape was used to mask inbetween colors and Tamiya sprays were used entirely. The red, yellow, silver and black were all sprayed on.