Do you have an original V8 radiator for the car? If so, you would just need a 64-69 style water pump for the correct hose connections. As far as aftermarket radiators go, try to check out what Mopar vendors that advertise in magazines.
My son's 65 Cuda with a 375 HP 340 uses a 22" 3 row AL rad. Cools OK on the interstate at 70-80 MPH at 80F outside.... which is no where near to using 375 HP BTW! The fan set up is going to be critical for the smaller 22' rad versus a later 26" rad.
How much HP in your 360 and what is it used for? Full time drag racing? Going to the grocery store?
The OEM a/c cars have a 3 row radiator, 6 vane pump, thermostatic fan, shroud, and different pulley system. I only have a 273, summer gets hot here 100+F, never overheated.