WHEELS AND TIRES
In the 1970s Michelin introduced TRX, a new wheel rim and tire technology intended to provide racing style low profile sidewall with ride comfort and improved road handling. Fast forwaard > TRX wheels and tires are today considered the Betamax of wheel and tire technology, so the owners of the many European cars built with TRX wheels have switched to Imperial wheel sizes.
Aurora Cars offered its buyers options; "turbine" style alloy or Dayton 72-spoke classic wire wheels. Both were available in 16" or 390mm TRX. TRX size tires are still made by Michelin and Coker Tire (as of 2014). If your Aurora has TRX wheels, you will find the prices for tires will puncture your hopes of maintaining factory-original authenticity.
GETTING INSIDE THE FENDER
Aurora suspension is modernized from Shelby's original transverse leaf spring and shocks. A-arms with coil-over shocks (see http://www.auroracobra.org/garage18.html)
This independent suspension necesssarily locates the wheel hubs further outboard than the Shelby originals, which means it's more difficult to keep your tires within the fenders. It requires wheels with more "offset," resulting in the wheel face positioned further outboard, and the tire further inboard. For 6-7" wide rims, 5" offset is about maximum.