How to set up a party planning business
If you will base your operations in NJ with most of the business expenses, business activity and clients, and probably assets, then it would make it easier to simply form your company in New Jersey. You could still register it in Delaware, but then you would almost certainly be required to register the company in New Jersey as Foreign Entity.
As far as entity type goes, corporation is a more formal business entity, with more formalities to maintain than LLC and quarterly filing requirements. LLC is also a more flexible entity from taxation point of view - by default it would be taxed as partnership (in your case), and you can also elect it to be taxed as S-Corporation (or even C-Corporation) if that would be more advantageous from tax perspective (however here you need a help of experienced CPA to advise you further).
Corporations have certain advantages that are beyond the scope of that answer, however in your case I would say an LLC would be a suitable business entity to run this business under.