A partnership is 2 or more people joining as one business. In such case, unless you file an LLC or incorporate, you will need to at least file a DBA and obtain an EIN. A DBA stands for "Doing Business As" and it is the registration of your doing business as trade name. For example, if you do business as "Joe's Fine Merchandise, " "Joe's Fine Merchandise" is a trade name. You need to register it with a clerk. If you do, you will obtain a DBA certificate that will help you create stationary and advertise with that name. If you file an LLC or Corporation, you can use the corp or LLC name to advertise and you will not need to file a DBA. If you are going to make any serious money such as more than $50,000 per year, you may want to form an LLC or coproration. It is the best to help you save on taxes and protect you from personal liability.
If you file as a sole proprietor, you will be liable for all business debts and liabilities. For example, you have a cleaning business and your employee steals from your clients, you will be liable personally. If you form an LLC, and the same thing happens, your personal assets, such as your home and car are protected. If sued, they can only get what the LLC has. If only $1,000 in the bank, that is all the plaintiff gets.
Even though they will tell you that Delaware or Nevada is the best state, the best state is actually the state you do business in. This simplifies the entire business.