car overheating and leaking.... water pump?

I have a 92 grand prix SE 3.1L V6:

So ive been leaking antifreeze at a decent rate on the street which kinda sucks... My problem is when im driving after about 5 minutes my temperature gauge will go all the way up and say "check gauges" and then after about 20 seconds it will go back to a little bit above the middle temp and sometimes repeat this if im driving for a while. Ive stopped and looked at my engine and steam and a antifreeze was coming out of an area down low im guessing it's the water pump.
My question is how much does it approximately cost to have my water pump replaced professionally or if my problems sound like something else could be the problem, a response would be greatly appreciated.

actually it might be your "Lower Intake Manifold Gasket" its a common problem on those engines i believe. my 2001 Pontiac Grand Prix SE 3.1 V6 just got new intake gasket put on

Yeah, i called a local mechanic and he also said it's probably something other than the waterpump and my other friend said something about an intake gasket. Is this a pricey fix, seeing how im taking it in on saturday morning itd be nice to know a general price range for these fixes.

conrads 700 bucks just did one yesterday

do it yourself very cheap like what under 100 for everything oil, gaskets, coolant ect

The intake issue affects 95-newer Vin-M and Vin-J, not the Vin-T engine in this car. The most common coolant leak issues on this car are the water pump and heater core (passenger's side) and the coolant quick connect nipple in the intake (driver's side). The water pump is mounted up high, toward the front of the engine bay. It's a very simple job (remove the belt and 9 total bolts), and scraping the old gasket off takes longer than actually changing the pump. The coolant nipple is on the driver's side just behind and below the thermostat housing. Removing the air intake tube will help in accessing it. Look for a black metal tube coming from the firewall to the intake. These connectors turn to mush after a while and crack, and will start to seep, then get worse and worse until they are spewing coolant everywhere. They normally don't start leaking until the car is warm and the cooling system is under pressure.

hmm could be the heater core because the leaking is coming from the passenger side. Also, this whole thing started when it got colder again and when id turn the heat on, it would be interchange between heat and cold air; mostly cold air tho.

I had the same problem with my car and it ended up being the coolant elbow was cracked! its like a $1-$3 part and an old friend who is a GP fanatic replaced it in about 40min!! Good Luck!