Car won't start, help with diagnosing?

I have a 1979 Ford LTD II. Only 61K miles on it. I'm pretty sure it needs a new starter. Most days i can start it up fine when it's cold but after running for 20-30 mins it will not start back up when shutdown. Once it's cooled it starts back up fine. I also noticed that on warm days, 60-70 degrees F, when sitting in the sun it won't even start initially. Just trying to run it by anyone with experience as to whether the starter is the issue. Oh also when it doesn't start and i am cranking it i can here a faint click about 1 second after i start cranking it. Don't know if that matters though. Thanks! :-)