Jennifer, define "good" primer. Most primers that are made by the paint companies are just thinned down versions of their paint. That is OK for some priming and a total waste for other work. Having a primer that is also a stain killer and sealer will give you a better finish with less work. The more that you do now to give your walls a chance to last a lifetime, the more probability there will be that they do. I agree with your contractor.