John Smith Esquire v. John Smith Attorney v. John Smith Attorney at Law

Esquire is a form of address used in different ways in the U.K. and the U.S. In the US, it is only used as a professional designation for a lawyer. Emily Post wrote,

“Esquire” is a professional designation in the legal arena—not a social designation. When you correspond with a lawyer, you have two choices: Write the person using a normal salutation (“Mr. Robert Jones” or “Ms. Cynthia Adams”) or put “Esquire” after the name, using the abbreviated form of “Esq.” (“Robert Jones, Esq.” or “Cynthia Adams, Esq.”) You would never use both the courtesy title of Mr. or Ms. and the professional designation of Esquire.

This applies to the US. In the UK, the term is a bit broader:

Many people in the United Kingdom no longer perceive any distinction between "Mr" and "Esquire" at all so that, in everyday usage, a distinction is very rarely intended.

So, if you are in the US, you can sign a letter John Smith, Esquire or John Smith, Esq. This is the form that I have seen most often in the US.

The terms attorney or attorney at law are names of one's actual position. For example, the editor of a magazine might have a byline that says "John Smith, Editor-in-Chief" and similarly a lawyer might use John Smith, Attorney at Law.

Since all of the terms are different (Esquire is a form of address, attorney is a position) they don't designate different levels of engagement in the profession. An attorney at law is an attorney who can appear before the court.

Note that some lawyers do sign using "Esquire", so if the lawyers around you are doing so, feel free to do so as well.

To address a letter, use Esquire or Esq. in place of "Mr." or "Mrs." To sign a letter, use Attorney or Attorney at Law since they denote one's position rather than one's proper form of address. To sign with Esquire would likely be like signing a letter, "Mr. John Smith."