How close are you to Boston? F1 Boston has both an indoor rental and outdoor racing track, thats a good place to start.
Entry fee's vary, but they're similar to autocross fee's ($25-50 per race per class). No license is required, but often you will be restricted to one of the slower classes until you've shown yourself to have the ability to drive. Slower classes means either a Yamaha or Briggs engine based class. Yamaha classes are based around the KT100 100cc two stroke motor running on gas+oil mix putting out anywhere from 12-20hp depending on exhaust, carb setting, etc. Briggs classes are based around either the old 5hp Briggs "raptor" OHV engine or the much improved and newer Briggs "Animal" OHC engine running on alcohol making about 10-15hp. A good ready to race setup with spares and tools should run anywhere from $2000-4500 depending on newness and how complete the package is.
Safety gear requirements are simple: closed face helmet, neck collar, gloves, and durable clothing that you'd be willing to get tossed out of the kart and go sliding in. I recommend getting karting specific driving suit, gloves, rib protector and shoes, I spent about $800 on my gear.
You will also need a way to get the kart to the track. I fit my kart in the bed of my truck, but a 40x48 HF trailer works fine for one kart if you can't fit it in your car. Obviously the sky's the limit on this one lol.
2007 Toyota Tacoma
2002 Kartmini Rotax TAG kart - F125
Never run out of ideas, traction, and real estate at the same time.