I agree with RAMAIR68, in most cases it's better to rebuilt, reconditioned and not replace your important car components. 100% stock system has been working for 50 years.
Some after market items are very desirable (EFI for example) and therefore worthy of installing on your driver. You just have to be carefull that you don't change one thing and bugger up something else.

Copper and brass is still the best material for a 60's car. Aluminum is lighter and cheaper that copper.
https://www.copper.org/applications/automotive/radiators/no_flux_history.html

Heating problems can be caused by an number of things, if you replace the rad with a new one (new or old school rad), it could still over heat due a other failed component(s). The next thing the guys will sale you is a electric fan. That noise making piece of [censored] technology don't belong on your engine. No way the electric pulls air thru your rad better than a stock flex fan or clutch fan (properly installed).

Your 50+ year radiator has to be serviced once in a while. You don't just take em when they leak, they need to be cleaned as well (remove buildup).

Start buy taking your old stock rad in for service and go from there.