If you have a partner, do you have some form of partnership agreement? Make sure that you print out the e-mails where both of you have discussed your understanding of the partnership. If you haven't had this type of discussion, I would sincerely advise that you talk about this now. Keep in mind that whether you succeed or fail is not the issue - you just want to make sure that you have everyone's responsibilities clearly outlined.

Regarding the legal structure. A DBA (i.e., doing business as) is usually something you get when you are going to be a sole proprietor and you just want to use a business name. So, Joan Smith doing business as Smith's Window Services. This way, if someone writes a check to Smith's Window Services, your bank will accept the check. An LLC is a legal structure that limits your liability. You have to file both with your state. You can do it with NY or NJ. They do have different laws but since you probably don't care at this point, doesn't really matter. The business can be registered anywhere - doesn't matter. It will matter when you have to pay taxes.

You can find links here for NJ: http://craftersbuzz.com/businesslinks.cgi?state=New_Jersey
and here for NY: http://craftersbuzz.com/businesslinks.cgi?state=New_York

You should get an LLC because that will actually give you some legal protection if someone sues you.

I would keep in mind that if you are providing services like Craiglist - they get in all kinds of trouble all the time. They've been sued by several states and others:
http://news.bbc.co.uk/2/hi/americas/7928148.stm
http://en.wikinews.org/wiki/Craigslist_sued_for_hosting_discriminatory_housing_ads
If you plan on growing, it really would be in your best interest to consult an attorney to make sure you get the proper legal structure.