1997 Saturn SL2 97 SL2 turns over but sometimes doesn't sta

I've just bought a 97 SL2 in mint condition with the exception of it sometimes not starting. It turns over and usually starts after a second or two. Sometimes I have to turn the key off and then try again and it fires right up. If I wait for the fuel pump to quit humming and the gas gauge to register, it's more likely to start. Yesterday, it wouldn't start on three tries with me giving no gas. On the fourth try, just as I moved the key back it fired. I plan to take it to a mechanic, but would like to have an idea of what they should look at. Thanks