Flushing with a garden hose isn't a bad idea, but as you are actually "replacing" the radiator, there isn't a tremendous amount of value IMHO. As mentioned, if you want to be thorough, those heater cores can use flushing as well, especially for a cooling system that hasn't seen frequent coolant changes.
If you are taking out the thermostat, replace it. 195 degree. I like stats from Jeep and also the Stant SuperStat.
Don't forget about the radiator cap. New ones are about $5.00 and are often overlooked.
Check all hoses. If they are older than 10 years old, consider a wholesale replacement. Hoses are inexpensive to replace and are one of those things that can lead to a tow, or worse yet, an overheat of your engine.
50/50 mix of coolant to distilled water and you are good to go. Verify strength with a hydrometer.