With a 180 degree thermostat, the engine SHOULD be running between 190 and 195. This is how it works, it won't run right at the stat temperature.
Anything under 205 normally is fine and will not hurt the engine. Overheating, IMO is over 230 on a warm day.
Put a new water pump on (they are cheap and yours sounds sketchy), and check your belt alignment with a straight edge.
I have electric fans only - Ford Contour fans - and my fans come on at 195 and off at 192. Rock solid water temp and the fans usually will only come on when sitting at stoplights and turn off within 10 seconds of pulling away from a light. 180 thermostat.