1996 Oldsmobile Aurora overheating problems?



Just got it today and drives really well but after a while it started to over heat. I popped the hood and the coolant was coming out of the cap for the coolant jug thing. (sorry dont know the term for it) I went to autozone they said it was the water pump wasnt working. Then i went to my mech. and he said it may be the cooling fan...(but hes going to check it tommorow) So i dont know whats wrong. Also the gauge was going up and then down and then settled at 225-250 degress. SO ANY ONE HAS A CLUE OF WHATS GOING ON?!!!
It's always fun when you realize there are a million things that could possibly be wrong with a car. I hope you figured it out.