Watson, it really depends on how complex you want to get.
For a very basic color wheel you could get by with a primary red, primary yellow and primary blue. By “primary” I mean hues of these colors that are neither warm nor cool versions of that color. Most art paints have colors that fit this description and they usuallu call them “primary red”, etc. You may be able to find color chips at the hardware store that are close, but you will need to keep in mind that the light in the hardware store may cause them to appear more warm or more cool than natural light would.
For your secondary colors in a basic color wheel ( orange, green and purple) you would choose chips that are the color you would get by mixing two of your primary colors. In this scheme, you would want to stay away from a green that is warm (that is, one that veers a little yellow) and also from a green that is cool (veers toward blue), same with your orange and purple. A little more complex wheel would add rings for tints (white added), tones (a bit of the color from the opposite side of the color wheel added) and shades (black added).
Many artists use a variety of different versions of the color wheel with different hues of red, yellow and blue for their primaries. Several contemporary artists do a good job explaining color theory: Steven Quiller is a painter who has several books and videos out- he demonstrates with paint.
Katie Pasquini Masopust has a class on iquilt.com that does a good job as well, but to do her exercises you need lots of fabric scraps- however, I think you could adapt her color wheels to paint chips. In that case, I’d suggest that you take as many chips as the store will let you have, making sure to get as big a variety of hues, values etc. as you can.
Hope that helps some.
Rob