I would start by contacting the Sports Car Club of America-SCCA- to see
what open wheel racing they are currently sanctioning. They can provide
you with the car specs.
It's been a while since I have been around this but Formula Ford was always
a good starting point. Depending on your budget it can offer good experience
and you can be fairly competitive at a reasonable expense.
Ideally the Toyota Atlantic series would be good if you have the funds to support the racing. Toyota Atlantic has a number of chassis available,
Renard being one of them. As usual the engine performance is in direct
proportion to your budget. The racing is very fast and very competitive. I
think it is still used as a stepping stone into F3,2,1.
For experience there are driving schools around the country that provide
classroom and seat time. Bertle Roos has one at Pocono that I did a few
times, it's good. Great instruction and driving experience to let you see if
you really want to invest in this. They also offer a racing series in their cars,
fairly affordable, very competitive that is a good way to learn before you
commit to building and running your own car.
As a guess, these days I'd figure $50,000.00 as a decent budget to get started. You can also shop around for used cars, they are available.
As I remember looking at 2 different cars, they were in the $25,000 to
$30,000 range to buy. Those were both Toyota Atlantic set ups.