1998 Pontiac Grand Am 1998 Pontiac Grand Am over heating.

Engine Cooling problem
1998 Pontiac Grand Am 6 cyl Automatic 173000 miles

ok ill try to make this as breif as possible.
had no real issues with my car. Then one day car engine wouldnt turn and so we had determined it needed a new starter, it was replaced and the car worked. Shortly after that the car was about to overheat. My car ride home it did and went into the red, I park my car to let it cool down. After turning off the engine the car no longer overheated the entire car ride. I bought antifreeze and emptied an entire gallon into the overflow resuivor and it didnt seem to fill it completely. After that it ran COLD. Not half way temp mark but lower unless ran for a long period of time. About a week later it started to get to the overheat mark. I put in more fluid and runs COLD now it seems to be getting hot again. I noticed a small puddle of fluid today under the car below overflow tank. The problem im having is now. When the car starts it either runs cold so to speak(under the half way marker) or it almost over heats. For example. Driving only 3 miles today, the car went from cold temp to half way mark in less then 5min. Then going 3/4 the way up then back down to 1/4 of the way after driving normal speeds (35mph) then heating up again this all within 10 min time. Turn off engine while waiting at light, turn it on. Went back up to just under 3/4 and stayed at that tempature. Any clues what could be causing this and where I should start as far as what to do?