For the '63 I restored, I bought a used Studebaker Avanti radio on ebay for $25. The seller didn't know if it worked or not, but I didn't need it to. There are a number of people you can send a classic car radio to, and they will restore it with modern electronics, make it stereo (which the originals weren't), Bluetooth compatible, install a port that you can plug an iPod into that will tuck up under the dash, and if you want, connect it to a CD changer that mounts in the trunk. I sent mine off to one of them. I didn't bother with the CD changer, which is an option I'd undoubtedly have selected if I'd done the restoration ten years earlier, but nowadays, with other ways to store music, why waste the trunk space?
If you go this route, you get an original-looking radio, with modern stereo sound. You change from AM to FM by turning the radio off and immediately turning it back on. I'd have loved to have an original Avanti AM/FM radio, but they're rare as not much was played on FM back then, and it was an option most people didn't select. The only one I've ever seen for sale was offered at $1200. I wasn't willing to pay all that just to have the FM markings on the dial.
I replaced the central speaker with one of those plastic tray inserts that Avanti Motors offered on later, stereo-equipped Avanti IIs, and that Dan Booth sells; and I put a pair of speakers in the rear shelf, and a couple of smaller speakers in the kickpanels (for which I had to fabricate a box). Unfortunately, the nature of the car limits the size of front speakers you can use.