These days, there even more choices when it comes to paint than airbrushes! Nevertheless, there are three essential types of paint for modeling: acrylics, enamels, and lacquers. Some people will tell you that they only use one type, but there is good reason to know how to use all three.
Acrylics are excellent for painting indoors. There are no harmful vapors to worry about (though you should still have adequate ventilation) and depending on the brand, the paints are nearly bullet-proof after drying. I use Tamiya, Vallejo, Italeri, and Gunze Sangyo acrylics whenever possible. Vallejo offers a wide range of colors though not many of them are truly 'color-matched' to any given color standard. The original Tamiya line was mostly generic colors as well, though they've been producing colors that now match various color standards. Gunze Sangyo used to offer an impressive array of color-matched acrylics in their Aqueous line, but they discontinued most of these in favor of a lacquer-based acrylic (isn't that a contradiction?) formulation. This lacquer/acrylic line is under the Mr. Color brand while the Aqueous line is now under the Mr. Hobby line. The Italeri acrylics are produced by Vallejo but come in larger bottles.
I still use enamels, specifically Testors Model Master paints, because I don't like to waste time mixing colors. I like to go to the shelf, get the bottle, and shoot the color, repeat as necessary. The Testors enamels are color-matched and easy to use. When I go to the store to pick up a new bottle of a given color to replace my three-year-old bottle of that same color, I know that the colors will match. For enamels, I use my paint booth to get the vapors outside.
I used to use lacquers for some of the bare metal finishes. With lacquers, if you spray indoors, it is vital you have a paint booth and adequate ventilation as these vapors will take you from zero to stupid in just a few minutes of exposure. There are more acrylic-based metallic finishes out there so you have choices.