The original questions have been pretty well answered, but here are a few thoughts about them.
"1. To buy a ham radio, do I have to have a license?"
No, but sometimes the dealer/seller may require you to have one, a CYA thingy.
"2. What is a good starter radio if I were to get a license?"
Depends on your wallet and what you think you would be comfortable with. I think the 'top of the line' kind of radio is certainly possible to 'start' with, you just have to read that manual more. Sort of.
"3. What is the average range of the radio with an average antenna?"
Depends on the band mainly. 'Range' is a terrible way to judge things! Depending on the band and antenna, there are no limits.
"4. How much does it cost to get a license and is it easy?"
The license fee is less than $20 and the license is for a 10 year period before renewal. Renewal is free. You are given all the question AND answers that will be on any test. There are several sites that have 'practice' tests, same questions as on the real test, take them as often as you like. It isn't absolutely a 'cinch', but it only takes some study/memory to pass any of the amateur radio tests. And naturally, if you understand what's being talked about it makes things easier (called studying). If you have no knowledge of electronics it will be more difficult than if you do, right? And a good percentage of the tests cover safety and rules. Both thingys that you really should know about.
The tests aren't "give a ways" but they are certainly not that difficult.
Have fun.
- 'Doc
PS - Testing in New Jersey (or any other state) is a matter of finding a club near you, or some other organization that does testing. The ARRL link is certainly a good place to start to find such a place. I'll bet that you can think of several other ways of finding one though.