Most coaches also have rackets your son can borrow and try out or can recommend a racket appropriate for his skill level and playing style that will fit your budget. There are so many different size and weights, it's best to get a recommendation from someone who is familiar with your son's playing style. Once you have a recommendation, shop around online. I once picked up a really great racket for $70 online because it was last year's model and was being phased out.
Something else to keep in mind in terms of cost though is that depending on how often he plays, the racket will need to be restrung from time to time. This can cost $25+, and must be done when the strings get worn or your son will be at risk for tennis elbow, shoulder problems, etc. You can tell when the strings need to get replaced when they no longer slide easily against their perpendicular neighbor. I play a couple times/week and replace my strings every 9 months or so. I love tennis, it is a lifetime sport, but it is expensive.