Too bad that the good open-wheel racing series are being canceled in the USA. Hopefully, if the F1 track in Austin comes thru, it will bring back new feeders series. Racing in Europe will remain necessary to go the top pro racing, but the US needs an affordable open-wheel series.
The Formula Atlantic (
http://atlanticchampionship.com), Mazda Pro Elan (
http://www.starmazda.com) and Indy Lights (
http://www.indycar.com/indylights) have more room in the cockpit than the FIA cars. Most people should fit in it.
It's usually around $3000 per racing weekend for arrive and drive an F3 type car. I have never seen an official insurance, I don't believe it will cover racing. There is usually a waver to sign your life off and a large deposit in case you break something, but these cars are pretty strong and easily repairable.