Keep the 180 thermostat, but buy a new one, I bought mine from the dealer, all made of stainless steel, so as not to rust.
If replacing radiator, I'd go and remove block drain plugs, thermostat housing, you're gonna change thermostat anyway, right? and flush the bee-jesus out of it, both sides of the engine. Same to heater core.
Then, to top off the job, I'd replace the hoses, clamps, rad cap, and belt(s). Might as well check the weep hole on the bottom side of the water pump for leakage, if evidence is there, calls for replacing water pump.
Now, the car is back together, and you're gonna pour in a 50/50 mix of good antifreeze/ distilled water mix. You might even add a recovery tank also, doesn't hurt.