I echo the sentiment re: being glad you found the tire issue before having an accident, or worse. I am not sure what kind of tire, or size, you are looking to get. I can tell you this, in my humble opinion it is better to get radials as opposed to bias belted tires. It is possible your Mustang had radials on them when you got it, and maybe even originally from the factory. But, our 1969 Shelby GT500 originally came with belted bias play tires. When we purchase dit the prior owner has a nice set of Mickey Thompson radials on it, and a decent, reasonable size as well (P235R60 x 15 mounted on Magnum 15 x 7 wheels). Bet, despite how well the Shelby handles and felt I just had to outfit it closer to what it originally came with rE: tire brand and model. So, I ordered some reproduction Goodyear PolyGlas GT F60 x 15 bias ply tires. When it comes to how the tires look on the Shelby I am very pleased. But....
One afternoon, not long after putting the Goodyear tires on the Shelby (and inflating them to 30 PSI cold) I happened to be out tooling around with my son. We were heading out somewhere together, and I had opted to take the Interstate, just because i wanted to "blow the carbon out of the engine" a little bit. Nothing too far over the top. In time our exit came up and I took it at a speed I had taken it at in the recent past with the radial tires on the Shelby. Nothing too wild, and nothing it could not have taken - or so I thought.
Whoa! Those bias ply tires did not stick to the pavement anywhere nearly as well as the radials had previously. I did not lose traction, but you can believe I put the tranny (C6) into second gear pretty quickly to help bring the speed down without risking locking the tires due to heavy braking. By feathering the brakes and throttle during gearing down, and running the outer edge of the turning radius along the edge of the pavement, I got lucky and managed to not spin out or go off the pavement, and had plenty of time to slow down even further once out of the turn I had been on. And, it was not really that severe a turn, nothing like a hairpin turn.
Anyway, the PolyGlas GT tires have a lot of life in them still, given how seldom the 69 Shelby gets out onto the road. But, if I am still around when they need to be replaced I will be looking for some OEM-ish look high quality radial if such an animal exists. Otherwise the next set of tires will be some contemporary high quality RWL radial tires for sure. I share this in order to underscore my suggestion you get aset of radial tires, as there is definitely a difference. And, yeh, do not get retreads! heh heh... FWIW....