accord start up problem

Hi. I have a 1990 honda accord and recently when I try to start the car
it just whines but doesnt start. If i let it sit for about 15-20
minutes then try again it starts up fine. This has happened about 3
times this month and im not quite sure what is wrong. 90% of the time
it starts up fine. Im thinking I need a new starter? Is there anything
specific I should check? If i need to replace the starter does anyone
know how much it usually costs? Thanks in advance.