Actually, you have more choices: a partnership, LLC, Corp, S Corp. All of them will work for you.
The differences between them relate to taxes, your personal liability, the cost and complexity of registering and maintaining the business, the governance rules etc.
In general partnership is the simplest and cheapest to setup, followed by LLC, followed by a corporation.
Broadly speaking people usually choose the simpler and cheaper business structure which in your case would be LLC or partnership.
However, this is a fairly complicated topic that is way beyond the scope of this answer so you should spend at least few hours reading about the basics of llc vs. corp vs. s corp. An excellent resource to start is: http://www.nolo.com/legal-encyclopedia/llc-corporations-partnerships and you can follow up by reading their book http://www.nolo.com/products/llc-or-corporation-CHENT.html which is exactly about that.
I don't know if I'm supposed to register my company or how to even startTalk to your chamber of commerce, locally. They will tell you the regulations.
Am I an LLC or a corpYou are nothing. Once you register the busienss you are a sole propietor. Once you register it as LLC or Corporation it is a LLC or Corporation. But every step requires paperwork.
Also, I'm located in New Jersey, USA.Pick up a phone register. Find out who is responsible in your local town hall. Go there (in person), get advice.
I suggest you find an accountant and talk to him/her about this. An accountant will advice you what the best legal entity is for you and your business, either LLC or Inc, or whatever.
You can also use an online service such as Legalzoom to help you with this or even do it yourself if you wish to do that. I also recommend you visit the State of New Jersey Business Portal, lots of useful information in their site.