The biggest problem you'll run into is trying to decide if its worth modifying the car to mount a modern stereo in it. For example, my '66 chevelle only has provisions for one speaker. A 6x9 (or 5x8 or 5x10, I dont remember, some odd oval size) dead center in the dash, firing up into the windshield. Back then most radio was mono AM only, so something as simple as putting door speakers in becomes a task of cutting metal out of those antique doors. Mounting a DIN sized h/u, same problem, it only has provisions for a knob-style radio.
If your dad wants a really trick setup, I know a guy out in Cali that modifies stock radios to accommodate FM reception, add preset buttons, even to control external equipment like an external cd player. He leaves the stock radio looking 100% stock, but he disassembles the radio, puts a computer board in it, and wires up the buttons and makes them programmable. For example, an AM-only radio out of a 1957 chevy can be made to get FM reception, its old AM preset buttons can become the play/fastforward/rewind/pause buttons for an external CD player, etc. Its not cheap, but its pretty much the ultimate setup for someone wanting to maintain their classic appearance. If your dad is interested, I can dig up the guy's contact info for you.