Yes try the Full Tilt rental first. Yes they rent out TAGs, typically a Leopard motor.
If your interested in getting involved, it should be a TAG kart, especially in the NJ, PA, NY, and New England states, region of the country. LO206 is not catching on.
As for pricing, do yourself a favor and buy a good used kart. IMO, a Tony, Compkart or Birel are your best bets for support and tunability in this region of the country. Yes there are other brands but these are by far the most popular TAG karts in the NJ region. I’m not a salesman, this is just an objective observation. Price $3000 – $3500 for a good used Tony kart or Compkart. As for motor, go with a IAME X30. Again, by far the most popular in the NJ region. It is also fairly easy to tune & maintain. You can find good used X30’s for about $2200 – $2500. As for finding good used equipment, talk with dealers in this region, i.e. Kaos Kart Shop, Full Tilt, J3 Competition. As for an X30, this EKN site has been a good option. I’ve personally bought 3 – X30’s from guys on this site and all have been a good experience!