What paint to use on particle board for a shoe rack?
Particle board is often covered with a plastic laminate instead of paint, but there's nothing inherently wrong with painting it. You don't want to glop on massive quantities of paint, but there should be no issue in painting it.
Use your favorite paint, so long as it's designed for wood, not plastics or metal. i.e., just about anything you'd get custom mixed that the paint counter at your local home improvement center.
If you want to go with a spray paint for a bit of an easier, smoother finish, that's where you'd want to be sure to avoid the ones that specifically indicate &quot;metal&quot; or &quot;plastic&quot; (though if they include those in addition to wood, you should be just fine).
Covering the particle board with a laminate isn't terribly difficult, if you do want to go that way. It simply takes some laminate and contact cement. How to do it would be the topic of a new internet search and/or a new question here.
Contact paper would probably not be a good material. In my experience, it would likely come off in your described use case far too soon, and it would be difficult to get good sealing coverage from the top to the edges to protect against water/snow melt/mud that might drip off the shoes and down the edges of the boards.