Sounds the engine coolant temperature sensor and thermostat,electric fan thermostat need to be replaced and then the quality/mixture of the coolant tested with a anti-freeze tester.Be sure that it's not the original old coolant and if it is change it asap but otherwise be sure it's mixed about 50/50.After that remove the reservoir or rad cap start it up cold and wait for the coolant to over flow that should force air out but you may need to shut it off top it off a few times after it cools down and bleed it a few times.I'd shop around for a water pump for it that isn't too expensive or go to a U pull auto wreckers and get one but regardless I'd probably change it.
Be sure to check all the cooling system look for severe rust or corrosion , check the metal lines/fins for softness or if you notice heavy green corrosion at the ends where the tubing bends etc it's time for a new or replacement rad.One way you can tell also is the purity of the coolant and if it's not clean that might tell you that the rad is rusted etc internally too.You could have a coolant system done performed on it but from what you're saying it sure sounds like the coolant system just needs a basic over haul.
Go over all the rad hoses/rad clamps, engine be sure that you don't have a faulty hose or any coolant leaks etc.Take a good look at the water pump pulley if it's wobbling or making odd sounds this would tell you that it requires replacing, also check the pulley make sure it's not leaking.
Make sure that the low fan is engaging just before the temperature gauge gets to half way if not the fan thermostat might be faulty or you've a faulty fuse/relay/fan/wiring.Normally if the A/C is turned with the engine running and the A/C compressor is working the high fan system will engage so be sure that it's working.
Hope that helps and best of luck.By the way if it was me and I wanted to save money etc I'd probably start with the temperature sensor, thermostat and testing the coolant's quality , plus checking the coolant system for any leaks etc and then work from there.Remember when it comes to temperature sensors they tend to corrode too and this gives the temperature gauge and coolant system improper readings, plus the engine won't run the proper temperatures.You want the whole coolant system up to par bec not only does the over all operation of the engine/transmission work a lot better you also save on fuel etc too.