This may sound like I am referring to the State of the Union address traditionally given by the president each year. Rather than engage in a ceremonial activity, mostly void of substance, delineating the perceived health and status of the LLC as a business form, the more important issue regarding the state of the LLC is how to choose the state in which it is formed.

If the state of the LLC is chosen wisely, there could be significant benefits to privacy which can be legally and effectively taken advantage of.

What is the difference?

Each state will require filing some kind of form provided by the state along with a filing fee and probably articles of organization. I have provided a link at the bottom of this page as a starting point to the online resources for the requirements, forms, and fees required by all 50 of the United States. There are also several commercial products available which may be consulted to help you to do the same thing.
Price
One major consideration is, of course, the cost. The cost of filing and maintaining the required formalities may vary greatly depending on the state of the LLC. There may also be extra fees for filing in a state other than where you conduct business.

Thus, the least expensive option is probably to simply choose your home state as the state of the LLC. Of course, if you are location independent, you might be traveling often and operating in many different locations and the costs of operating as a "foreign" LLC will not matter to you.

The other cost consideration is the trade off of time invested versus money spent.  The commercial products may save you time but will cost you more money.  Filling out the forms yourself will save you money but take time.

Many states are very picky about how the formation documents are prepared and so significant headache may be saved by having a stuffy professional prepare the documents, trading off an increased cost in preparation for avoiding the risk of improper preparation.

If you haven't had much experience dealing with a government office, think about how fun a trip to the DMV always is and what price you would pay to have someone else show up and wait in line for hours and deal with the usually unhelpful and sometimes rude staff.  My dealings with filing with the secretary of state of some states has been comparable to the stereotypical DMV experience.

Legal Protection
The laws of the state of the LLC can effect greatly how you are able to conduct your affairs and how favorably you and your LLC will be treated.  The combination of formal requirements, tax treatment and other legal frameworks combine to to create an overall legal environment in which your LLC will operate.

For this purpose, the states of Nevada and Delaware are generally known as the two states with laws most favorable for LLCs.

Privacy Protection

All states require some disclosure of information to choose their state as the state of the LLC. By far the state that requires the least disclosure of personal information is New Mexico. 

An LLC is already a great way to protect your privacy, regardless of the disclosures made to form it.  The added privacy that a New Mexico LLC offers makes the protection that much more powerful.

Conclusion

The state of the LLC you form is an important consideration in optimizing your privacy protection.  Taking into account these, and any other considerations you may have, will help you to make the best decision of where to form your LLC. 

Many of the other considerations for choosing the state will depend on where you intend to have your tax domicile and other things found in the book How To Vanish.  You will want to find an attorney to help you form your LLC.

Find the Secretary of State’s Business Search for all 50 States

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Starting Point for Forming an LLC in All 50 States