What colors should I buy to start out with?

The best primary colors to use for mixing the widest possible range of other colors are called printer's primaries. Though we learn in school that red, blue, and yellow are primary colors, a much wider range of possible colors can be obtained by using cyan (turquoise), magenta (fuchsia), and a pure light yellow as the three mixing primaries.

Yellow. Among Procion MX dyes, the best all-purpose yellow is MX-8G, which Jacquard and Dharma Trading call lemon yellow and PROchem calls sunshine yellow. (ProChem's lemon yellow is a different color altogether.)

Blue. The best all-purpose blues in the Procion MX line are turquoise MX-G, called turquoise by most companies, blue MX-G, called cerulean blue, intense blue, or super blue, and blue MX-R, called sky blue, basic blue, clear blue, or royal blue. Turquoise and sky blue should be used in double the concentration of other dyes, by volume, for similarly intense results.

Red. Most beginners use MX-8B (called fuchsia) for their red, but MX-5B (called light red, clear red, or mixing red) is an excellent alternative which many prefer. Both are rather bluish reds. (Add a touch of yellow to get scarlet.)

Black. Consider getting a black, also, for tie-dyeing. A bit of black in a design can make other colors nearby look brighter by contrast.

Once you have decided that you really like dyeing, you'll probably want to get to know some of the other available in the same series of dyes, whichever series you are using. (I maintain a list of the pure, unmixed colors in the MX line of dye.) Each pure dye has a different character than the others. You may wish to skip buying mixtures, however, as you can always mix them for yourself, if that's the sort of thing you like to do, saving both storage space and money.