If a designer wooden high chair is out of your budget, look to yard sales to find a well-loved chair that's seen better days. Be sure that the chair is sturdy and size appropriate for your child, and be sure to test for lead before doing any work on the surface.
Allow the chair to dry fully from the washing before priming. Apply primer using thin, even coats and be sure to get primer into any ridges or woodwork details. Allow the chair to dry overnight.
With spray paint, wearing a respirator mask in a well-ventilated area is always a good idea.