I see this kind of question a lot. There are several issues you need to consider:
Choice of entity:
Your basic choices are C corp, S corp, or LLC. Each has its own advantages and disadvantages.
LLCs became really popular in the last 10 years because they have certain flow-through losses and depreciation that fits really well if you have a high income and own real estate.
C corps are big-boy corporations. The major advantage for IMers is that C corps can have foreign owners. So if you live in India and want to make Internet Millionzz, you can use a C corp to create an American identity. The disadvantage is that you are supposed to have annual shareholder meetings and board meetings. And keep minutes. And keep those minutes on file. If you neglect to do this and get sued, your corporate protect evaporates in a puff of shredded paper.
S corps are small corporations. No foreigners need apply. But, somewhat like an LLC, they are pass-through entities. For most people, this is the best of both worlds. You get the flexibility of a corporation and the benefits of pass-through losses (if any) like an LLC.
*Note: you can form an LLC and then elect to have it treated for tax purposes as an S corp (or anything else for that matter).
Location of incorporation:
Now you said you live in NJ but want to incorporate in DE.
First off, DE is where big banks and such incorporate because DE has some favorable laws and treatments for public companies. These reasons do not apply to you and me.
Other people like to incorporate in FL, TX, WY, and a few other places because there is no state income tax in those states. Then there are those who really like NV and WY because you can do stuff like issue bearer bonds.
But! If you are an owner of this corporation and live in NJ, NJ will come to you looking for its piece of your income from that corporation. So it's largely a moot point.
Also, if you incorporate out of your home state, you will need an address in that state and someone there to receive notices and mail. That's called a registered agent. This usually costs somewhere around $150-$250 a year. Unless you are making a ton of money, it's usually not worth it.
There are techniques you can use to minimize this tax burden like income splitting (if a C corp) and just expensing as hard as you can before retaining earnings or making a shareholder withdrawal.
Where to get everything set up:
You can search online for some company to incorporate you. I do it myself, if you are interested. You will need an address in the state, a person designated to receive mail, your name, your address, your SSN, plus whatever fees are involved.
Or you can follow the DIY and read through the secretary of state's site in whatever state you incorporate in.
Either way, when you're done you'll get articles of incorporation (or something similar) and a FEIN (tax ID). Those two will allow you to get bank accounts, credit cards, etc etc.
If you have any more questions, let me know.
