Do you know how the ink will slide off if you touch it on whiteboards using a dry-erase pen? Plastic miniatures are basically like that, like a dry-erase board. A marker will make permanent marks on paper, though. Primer paint is basically a layer that acts like paper onto the surface of the mini so that your dry-erase pen (paint) sticks instead of sliding off. Most paint doesn't include bonding agents that would allow it to stick to plastic. Primer is designed to be thin and stick to plastic and present a paintable surface.
Primer tends to come in spray cans. Flat gray is the easiest to use, though white and black have advantages.
Many use Rust-oleum brand primer, but any thin primer will work. Many prefer not to use Games Workshops Citadel primer, though the Contrast Undercoat primers have received some praise. A single primer can cost about $20 from Games Workshop or $5 from another manufacturer. One example is: http://www.amazon.com/Rust-Oleum-249115-Painters-Purpose-12-Ounce/dp/B002BWOS4Y/
Paint Brushes
Use these to apply paint to your minis after they have been assembled and primed. Buy cheap ones at first, as every painter ruins their first set or two. Expensive paintbrushes can wait for later. A cheap set like this should run you about $10 USD: http://www.amazon.com/gp/product/B014GWCLFO/
Miniature Paints
Miniatures Paints
Brands: Vallejo (third-party) and Citadel (Games Workshop) are the two most commonly used paint brands. Both are excellent, and there are other brands as well.
Paint Types: Citadel has paints that have different physical and visual properties. A brief description of their paints by type:
Base: This paint is very powerful and not translucent. It should be placed on the primer to make the main color for that section of the mini. It is very commonly used.
Layer: This paint is semi-transparent, and you layer it over the base paint to change the color of the paint. Commonly used.
Shade/Wash: This paint is very watery and designed to sink into crevasses in the mini, bringing out detail and adding feel to its recesses. It is very commonly used.
Dry / Drybrush: This paint is designed to be used with a dry brush, sticking to upraised parts of the mini, casting its protrusions into relief. Sometimes used.
Contrast: This paint is meant to fill the role of Base, Layer, and Shade/Wash all in one go. It is watery like Wash but colorful like Base. Use it over Contrast Primer or as a kind of Shade/Wash. It is sometimes used.
Technical: This paint has texture particles mixed into it. It is supposed to be painted onto the base around the miniature's feet to give the ground a feeling. It is somewhat commonly used.
Air: Paint to be used with a powered airbrush. Specialty product, rarely used.
First, you'll likely want to pick 2 Base Coat paints for your two main colors. You'll likely want 1 Shade/Wash paint to accentuate your miniatures' details. You will also want 1 moreBase Coat paint for your weapons and perhaps for armor trim, typically grey or black, though it varies from army to army, and some like to use one of their two main colors for this. Depending on what kind of minis you have, you may also desire 1 Contrast Flesh paint to easily paint their faces and hands.
In the future, as you go, you'll find you'll want to buy additional paints for gems, banners, extra cloth ribbons, extra details, eyes, armor trim, highlighting, dry brushing, exposed metal, weathering, and so on.
Cost: This setup (3 or so Base Coats, a Shade/Wash, and another color of some kind) will likely cost you $40.
Painting Resources
Citadel Colour: Games Workshop's Citadel Colour is an invaluable guide for getting started with Citadel paints. You can access it here: http://citadelcolour.com/