I agree, change out the radiator, esp. if the coolant has not been changed every 2-3 years.
If you can wait, you can have a rebuilt radiator from Reseda Radiator that specializes in rebuilt radiators and will give you core-credit for about $125.
Also, change out ALL hoses (heating & cooling) and the thermostat like you mentioned if they haven't been changed out in 2-3 years.
BTW- I hope you're replacing the waterpump with an actual Mercedes (new or rebuilt) waterpump. Aftermarket ones are not built to the same tolerances, AND the impellar blades are not shaped like the factory ones for better water circulation.
1988 360TE AMG