Moving to America with a criminal record

I cant speak to your issue with confidence but I would suppose you start at the US embassy.

I think you will find this link useful, which discusses crimes which can make you inadmissible or ineligible to become a Lawful Permanent Resident

http://www.nolo.com/legal-encyclopedia/ … sible.html

Here is a summary of the crimes or related activities that the U.S. Citizenship and Immigration Services lists as inadmissible. Note that not all of them require an actual conviction in court to make the applicant inadmissible. Do not rely on this list alone in assessing your immigration situation; get help from an experienced immigration attorney.
•    Conviction of a crime involving moral turpitude (but not a purely political offense). This includes any attempt or conspiracy to commit such a crime. It excludes crimes committed when the person was under the age of 18 years, so long as the person was released from jail more than five years before applying for a visa or other immigration benefit. It also excludes crimes for which the maximum penalty did not exceed one year in prison and the person was not, in fact, sentenced to more than six months in prison.
•    Conviction or admission of a controlled substance violation, whether under U.S. or foreign law. This includes any conspiracy to commit such a crime.
•    Convictions for two or more crimes (other than purely political ones) for which the prison sentences totaled at least five years. This multiple-offense ground of inadmissibility applies whether or not the convictions came from a single trial and whether or not the offenses arose from a single scheme of misconduct or involved moral turpitude.
•    Conviction of or participation in (according to the reasonable belief of the U.S. government) controlled substance trafficking. This includes anyone who knowingly aided, abetted, assisted, conspired, or colluded in illicit drug trafficking. It also includes the spouse, son, or daughter of the inadmissible applicant if that person has, within the last five years, received any financial or other benefit from the illicit activities, and knew or reasonably should have known where the money or benefit came from.
•    Having the purpose of engaging in prostitution or commercialized vice upon coming to the United States, or a history, within the previous ten years, of having engaged in prostitution.
•    Procurement or attempted procurement or importation of prostitutes, directly or indirectly, or receipt of proceeds of prostitution, any of which occurred within the previous ten years.
•    Assertion of immunity from prosecution after committing a serious criminal offense in the U.S., if the person was thus able to depart the U.S. and has not since submitted fully to the jurisdiction of the relevant U.S. court .
•    Commission of particularly severe violations of religious freedom while serving as a foreign government official.
•    Commission of or conspiracy to commit human trafficking offenses, within or outside the U.S., or being a knowing aider, abettor, assister, conspirator, or colluder with such a trafficker according to the knowledge or reasonable belief of the U.S. government. Also inadmissible are the spouse, son, or daughter the applicant if they, within the previous five years (but when older than children), received financial or other benefits from the illicit activity and knew or reasonably should have known that the money or other benefit came from the illicit activity.
•    Conviction of an aggravated felony, if the person was removed from the U.S. and seeks to return (this ground of inadmissibility lasts for 20 years)
•    Seeking to enter the U.S. to engage in money laundering, or a history of having laundered money, or having been (according to the knowledge of the U.S. government) a knowing aider, abettor, assister, conspirator, or colluder with money launderers.

Per the above information from BackgroundSearch.com, Driving license points and fines are not cause to deny you a work visa or a green card. 
Summary:
1) You did not go to prison and you were not convicted of a crime of violence or moral turpitude. Your driving points and fines will not keep you out of the USA. 
2) Whether you are in the USA or in your home country, you could try to get hired by a company in the USA and have them apply for a work visa, and then you can start fulfilling the requirements for a  permanent residency.
3) On your B2 visa, you can only stay in the USA for 6 months at a time.  You should make good use of the time to unofficially seek employment or conduct interviews.  In between interviews you are a tourist, and it would not hurt for you to have a site seeing plan.  You should use the internet to research companies that will petition for an H1B visa for people with your qualifications.  You job search should be done both in your home country and in the USA.

Hi
In my experience it's not difficult to get a US marriage based greencard  with a UK criminal record.
(I had 12 convictions including ABH, weed, shoplifting and Eco protest related charges)

The good news is the 601 waiver is to help you get in not keep you out. It's for people who have "reformed" so provide lots of character references.
Your case sounds very minor to me actually.
Firstly obtain your UK  police records to see what you really have to declare.

You have to apply for the I 485 first and then they decide if you need the 601 according to the police record.
All that time you can live and work in USA.

Good luck