If you want a good, accurate looking car from a current manufacturer that can be a solid performer when correctly built and sorted, look at used cars from Unique Motorcars (highly recommended as one of the better brands) and Hurricane, if you can find any in your price range. There are other great cars from ERA, Superformance, and others but these will probably be above your stated budget. If you are not fanatical about accurate appearance, there will be a few FFR (Factory Five Racing) cars with IRS and plenty with solid axle rears that will be nicely finished and within your price range. The newer FFR MKIV has a much more accurate body shape, but there wont be many if any lower priced examples on the used market yet. Backdraft makes a popular, well finished car with a stretched wheelbase and a unique body shape - you may find a used one at your price point.
Others will chime in with more recommendations. Look at the used Cobras on
427 Cobra Country--Ford AC Cobra replica manufacturers SUPER-SITE for those brands and others that will be mentioned here.
E-M built some good cars with both Jag and Corvette based rear suspensions if you can find them. Highly respected manufacturers that are no longer in business like Butler and Contemporary Classic should also be watched for - some reasonably priced gems occasionally show up for sale.
Be patient; settling for a sub par Cobra that burns rubber and makes big noise through the pipes but can't keep up with a Honda Prelude on the road because of crappy brakes and suspension could turn a rewarding ownership experience into a huge disappointment.