Federally, you must be age 18 to buy a rifle (21 for a handgun).  Local/state restrictions may be more restrictive.  I highly recommend a Ruger 10/22 or Remington 597.  I like the magazines for the 10/22 better.  They are cheap and accurate.  

The law does not differentiate between various types, other than machine guns and guns with short barrels--<16" for rifles, <18" for shotguns.  This is like comparing a race horse to a plow horse.  A RF tends to shoot a 40 gr. bullet at about 1300 feet per second (fps).  Centerfire rifles tend to shoot a 55 gr. (or so) bullet at about 3200 fps. or more.  Basically the RF is good out to about 100 yds max, and that's stretching it beyond 50 yds.  The centerfires are good to about 300 yds.  These are broad generalities--the .22 Hornet caliber cannot really be compared to a .220 Swift.  Of course the .223 Rem. is a good all-around caliber that happens to work in most AR-15's.  [:D]They are great--about the best, if you want a very expensive rifle, and appreciate that.  You don't gain much in terms of performance.  They are a little more accurate than other bolt actions tend to be, but not much.  There main appeal, IMO, is snob appeal.  Top quality just matters to some--if that is the case with you, this is the one for you.  Enjoy!!  

A semi-auto action does not cause you to fire more rapidly with less consideration of the target between shots - this comes from personal discipline.

Having said that, I would recommend a bolt action for your first rifle, and the .22 rimfire cartridge.

In my opinion, you would be served very well with an older Remington rifle from the 40's or 50's, such as a 513T, 521T, perhaps a model 37 (these all have target rifle features, the 513T and 37 are true target rifles, although not competitive these days).  Kimber's have a spotty quality record, although they are generally good, I wouldn't recommend one as a first rifle.

Your more pressing need is to get hooked up with a shooter or club that can allow you to get hands on experience.  The college you choose may have a rifle or shotgun team, or a ROTC unit (however ROTC is not just about shooting).

A very good source for initial training are conservation department programs in many states; contact the state or local offices and ask what they have to offer.

The following link will yield several clubs and instructors in the NYC region -

http://www.nra.org/frame.cfm?url=http://www.nrahq.org/safety/education/basictraining.asp

You should also look round the NRA web site at

www.nra.org

You are on the right track; keep looking around, learn what is right and what is BS, and start shooting.

One other idea - consider attending camp at the NRA Whittington Center in New Mexico - you will get exposed to all of the shooting disciplines.  Use caution, however - the clean air, open spaces, and low population density might change your life.

Having read this thread and your requirements and considering that this is your first purchase I without reservation reccomend that you purchase a Romanian M-69 training rifle.  They are rediculously accurate for a $59 rifle and are quite well made.  This is a good entry into this sport.  After years of very expensive and hungry Semi Auto rifles I purchased one of these this fall when they were on sale at a local sporting good store.  I liked it sooo much that I went back and bought another to put away for my son when he is big enough to learn.  This is by far the best value in .22 rifles going and is a great way to start.

Low investment, high quality, big fun.

ALso .22 ammo costs about $10 per 500 compared to about $50 per 500 for centerfire surplus or russian import ammo.  BTW plateshooter taught me to shoot a scoped .22 rimfire accurately out to 200 yards, amazed even me.