Most persons qualifying for permanent residence through employment may apply for green cards without leaving the U.S. You must demonstrate to the INS that you qualify for adjustment of status and that you do not fall within any of the "excludable" categories. For example, persons convicted of serious crimes, terrorists, and those who test HIV-positive seldom qualify for green cards.
Your spouse and children may obtain green cards at the same time as you do. Many INS districts now waive personal interviews.
You may be able to qualify for a green card in one to two years if you are exempt from the labor certification requirement. If labor certification is required, expect to wait at least three to four years to become a permanent resident.
A little advice about attorneys: Most persons who seek H-1B visas and permanent residence through employer sponsorship do so with the aid of an attorney. This is wise because immigration laws and procedures tend to be complex. Do not select an attorney solely on the basis of a referral by a friend or a colleague. Shop around not only for price but for quality. Ask for a copy of the resume of each attorney or law firm that you consult with before choosing who will represent you.