Al,
While there could be a problem with your ignition circut, I say replace the starter. I'v had similar problems on other cars I'v owned. Unless there are some bare wires around the starter, that type of problem is usually related to the selenoid (spelling?) -which you may be able to replace in order to save a little cash. But, I like to think about longevity. How much work does a starter do? A whole lot... In my opinion, the safe move is to replace the entire starter because you still gotta take it out for any repair you might do in the first place. In the end, a little more costly but the benefit is peace of mind. Peace, Jon