First decide if you want to build the car from a kit and if so, how much of it are you willing and prepared to do. It will require a place to work on it comfortably and an assortment of tools to accomplish mechanical assembly, fabrication and bodywork. A good number of hours is also required. If you choose not to build and can do some work, a turn-key minus car might suit you wherein you would only have to purchase and mount/plumb/wire-in the engine and transaxle. If you are unable to do the work, for whatever reason, you'll need to scour the ads in this forum, Club Cobra, Cobra Country, e-bay,etc. and try to find a sorted out, running car that you can afford. If you choose the latter, make sure you're aware of the motor vehicle laws in the state you're going to register the car and whether or not the chosen car will meet the requirements.
If you build or buy, you'll have to weigh the merits of a space frame car (Tornado, Bailey Edwards,etc) against a monocoque chassised car (Superformance, CAV, RCR,etc). Building will give you a wider envelope in this category as when purchasing the complete car, your choice of style may come up for sale less frequently.
Now for the Big Nut - budget. You'll have to allot, as a minimum starting point, about $65k. You can find an occasional complete finished car for that figure but it may be a l-o-n-g wait. Turn-key minuses start around this point so add at least another 15K for engine/trans. Building from a kit will end up around this as well when you figure in those items plus body work and paint. The advantage to building in this case is you can cough up the dough gradually, as opposed to a couple payments with the tk(-) and one big 'ouch' for the running car.
Do your homework, read up by perusing forum posts, see which manufacturers have good customer ratings and get some clear cut, realistic goals. Good luck and welcome to the forum. A.J.