Yes, it would be much easier for you to marry in the US, apply for a spousal visa and then start the UK job once you have it.
That way the company wouldn't need to do anything except employ you and you would not need to pass the resident labour market test or be sponsored by the company for a work visa
If you will be marrying a UK citizen anyway then work visa sponsorship should be a last resort in the case that your husband cannot meet the financial requirement for a spousal visa and your only option for moving to the UK is to get a work visa because it is impossible for you to qualify for a spousal visa.
Edited to add: if the company were to sponsor you, they would first have to apply for a sponsorship licence which would cost them over £1,000 and generally takes at least 6 months to be approved, then they would have to prove you met the requirements for a company transfer visa, then apply for a sponsorship certificate for you, then you could finally apply for a work visa. You'd probably be looking at not being able to move to the UK on a work visa until late 2014 if you did it this way.
Or you could just get married, apply for a spousal visa and start working for them immediately, as if you were a UK or EU citizen. If you were to do this, you could probably be living in the UK and able to work for the company within a few weeks of the wedding.