Don't know about your particular car, of course, but whitewalls were an extra-cost option on all models. The full wheel covers were also a separate option... so any combination was available... blackwall or whitewall tires, with either full wheel covers or the smaller "hub caps". In addition, I _believe_ there was yet another option with the hub caps, a trim ring.
I had a '63 Starfire for awhile and it had the old bias-ply tires on it, and it drove pretty wonky... if you plan to drive your car much, esp any kind of distance, like a road trip to a meet, I'd go with conventional blackwall radials. The only glitch is, the aspect ratio on the original tires, that are probably something like 7.50 or 8.00 x 15s, was 80 or 85% (I forget which, but something like that), and the P-metric tires available now are 75% at best, so they are generally shorter, which will throw the speedometer off. In order to get a p-metric tire close to as tall as the originals, it's gonna have to be a really wide one, say 255, 265, 275, something like that (I don't know how wide they go) and that may not fit the rear wheel wells without rubbing, or the fronts without rubbing on the inside while in a turn. bleah. You might look on
www.tirerack.com and just see what kind of 15" tires are available.
One thing you could try is to buy a used tire and try it and see how it fits... 215 sounds pretty small to me - I'd go with at least a 225 if it will fit - actually, I'd put the biggest P-metric on there that would fit, because, as I mentioned above, even that won't match the height of the originals... but the closer you can come to that original height, the more accurate the speedo will be. I'm not sure what's involved in recalibrating the speedo on the '50s cars, assuming it can be done at all.
Good luck - hope this helps a little... all this tire business can be a bit of a problem with owning an older car - some of the '60s cars are even more of a pain because they had 14" wheels for that longer lower look, but you can't get contemporary tires for them that look right... and if you go to 15" wheels, you can't use your stock wheel covers. Buddy of mine has a '75 Ford F-250 pickup that came with 7.50x16 tires or something like that and he has the same problem... can't find a replacement tire that's tall enough... or maybe they're 16.5s, even worse. I've always thought that what I'd do if I scored another '60s car with 14s would be to spring for a set of vintage aftermarket 15" wheels like Cragers or Americans, put a set of Radial T/As on them, consider them a vintage aftermarket customization and take the hit in favor of driveability if I was gonna have the car judged.
By the way, if you do go with today's tires, I'd get a BF Goodrich Radial T/A.
Regards,
Doug