For rally, the SCCA is a good organization to start. Can start doing RallyCross without having a rollcage, just meeting the minimum safety standards of the groups, and having the proper helmets and equipment.
Every year I help my friends out with their cars at the Cog Rally, mainly go to spectate, but usually end up helping bend control arms back to semi-straight, or rolling cars back onto their wheels so they can be loaded onto trailers for the ride home.
That's my friend Moody's old Rally Car, mmmmm, I can just hear the massive turbo spooling up on that monster. It's extremely fun, but an extremely expensive form of racing, be prepared to dump a couple grand into just getting a roll cage, and undercarriage plates installed to spec, and then have another couple grand saved up each time you go to race, because something can and will go wrong.
In Colorado we have the CHCA (Colorado Hill Climb Association), there might be similar associations where you live (generaly cheaper to get involved in sometimes more fun and exciting races than with the bigger clubs).