Adjusting from L1 Visa to Marriage Green Card

Hi,
I've tried searching this topic in the FAQ's but with little success.

My husband is a UK citizen. I am a natural born US citizen. He still resides in the UK, while I am in the US. We were married in the Bahamas two months ago, then each of us returned to our respective countries of residence.

His L-1 Visa was granted this week and he will soon begin work in the US. He will be back and forth between the US/UK over the next few months for conferences, client visits, etc. Since we are now married, what are the proper forms to file to adjust his status from L-1 to a permanent resident? Should we go the marriage route in the event he changes employers in the future?

Thanks in advance!

I would file an I-130.

Thanks. Is that the only form I would need to complete, and once it is filed would he have any issues with traveling in / out of the US?