As transportation goes, there is a new train system that is directly connected from JFK... if not, there are also numerous buses that stop at the terminals. (I used to work in the Starbucks in Terminal 4 back in my high school days and this is how I commuted.) Not sure how much the new train is, but the bus is $2, with free transfer to the subway or another bus.
Like someone else said, parking in NYC is a b!tch, sometimes you have to circle your neighborhood for like 30 minutes to find a spot (hope you are good with parallel parking cuz that's all there is).. and yeah of course there are those trash days. And you probably don't want to deal with driving a car in NYC either, it is aggressive as hell (although you are from Detroit, so it shouldn't be too much worse in NYC. You do get used to it I guess.) Personally I never drove a car until I went away to college.
JFK is in Queens... not sure if you want to live there or another borough, but I know the rent prices in Queens ranges from at least $1000 for one bedroom, to $1400 and up for 2-bed.
I never flew in or out of JFK, but I did fly in that Class B for about a month doing aerial survey over NYC... it actually wasn't as bad as I expected! I actually enjoyed my experience there.. seeing all those heavies so close-up like every minute! The controllers talk a little faster, but you get used to it after the first day I guess. Otherwise I only got yelled at once during that month... (but he was really nasty with me that one time.) They really weren't unfriendly at all... at least, they were polite enough to almost always "Good day"-ed me.. lol.