Do not attempt to dive in to AMA 600 racing as a start. It's complicated, expensive, and YOU MUST BE FAST ENOUGH TO QUALIFY! That means make no less than 115% of the pole speed (factory guys, factory techs, factory equipment) and is actually challenging to do.
Here's what you want to do. Buy a cheap (not ragged) ex race bike. It is already prepped! Pour your money into good rider safety gear. Book some track days and maybe a school (I recommend Jason Pridmore's Star School, he is an ex AMA rider and can point you the right way), burn thru some tires, evaluate your riding and desire level, then check into your local regional racing club (WERA, CCS, CMRA, LRRS, CMMRA). Find out from that regional club what it takes to get licensed, what the fees are, how much travel expenses you need, how to get thru tech ect. Most clubs have a "new rider" or Licensing requirement school, some accept your participation in a racing type school like Pridmore's or Lone Star Track Days, Penquin School ect. as a qualifying school.
Do some local/regional races to get used to the routine, know what you need to equip yourself with, how fast you need to go, how to set up a bike, ect. Then evaluate if you have the speed, talent, desire, and budget to go to the next level. If you do gather up what you need get AMA licensed, and go try and qualify.