Nope, you don't need a permit for most nonvenomous non-threatened lizards in the US, with the exception of native species or large varanids (monitors) in some cities or states.
Crested geckos are a great species to start out with. Their care is pretty basic, they reproduce readily in captivity, and they're pretty forgiving of basic husbandry mistakes. Leopard geckos are also an excellent starter lizard. Chameleons less so, since they can have very specific humidity, temperature, and UV light requirements. I recommend starting with either a crested or a leo, it simply depends if you want an arboreal, tree-dwelling species or a ground-dwelling one. Cresteds and leos need pretty different tanks because they prefer different habitats.
If you want to get into crested geckos, I highly recommend buying the book
Rhacodacytlus: The Complete Guide to their Selection and Care available for $40 on
Amazon.com. If you want to try leopard geckos, then I suggest
The Herpetoculture of Leopard Geckos, available for $20 on
Amazon.com.
Choosing a reputable, trustworthy breeder with quality animals is key to having a successful reptile collection. You're off to a good start by joining a reptile forum. If you see critters for sale on here that you like, you can check the
Board of Inquiry to see if the seller has positive reviews. Trader and karma ratings under their name in each post is also very helpful in learning who you can and can't trust. For example, those two green squares under my name over there <---- mean that I have more positive karma than negative, and my 5 trader ratings mean that I've made 5 positive transactions, either as a seller or a buyer, with certified Fauna members.
The important thing to realize that these animals can live up to 20 years. If you plan to breed, you'll need easily 2-3 times as many cages as you need for your basic collection of adults. A single female leopard gecko, for example, can lay up to 10 eggs a year. That's 10 different cages you'll need for the babies until they're old enough to sell or give away. That's why many of us choose to house our reptiles in heated
reptile racks.
The price of feeding reptiles can get quite expensive depending upon how many you own. Crested geckos are nice because there is a pre-made
commercial diet available for them. Leopard geckos will eat mealworms, crickets, superworms, or roaches. I raise my own Dubia cockroach colony now, which has saved me about $100 this past year in feeder costs.
I hope this answers some of your questions! First and foremost, you should research the species you wish to purchase by examining caresheets on the internet, or purchasing the books I've listed above. I personally like having a library reference, but caresheets are available by the dozens for free.
