Your case is somewhat similar to that of my husband... he too is here on an L1 visa (and has been here in the past on H1). Once you are married, your spouse can file I-130 (Immigrant Petition), I-485 (Adjustment of status/LPR) along with I-693 (Medical), and an I-864 (affidavit of support from your spouse). As you will read in the instructions for I485, it
must be accompanied with I693 and I864/I864A, however, you may optionally, also file I765 (authorization to work also known as EAD) and I131 (Advance Parole - ie, permission to leave and re-enter the country while your I485 is being processed).
We (my husband and I) knew very little about the process and made a mistake of filing only I-130 and after 3 months, only now we are preparing to file I485. However, we are not filing any I765 or I131 because my husband's L1 is still valid for another 15 months (and we are hoping that by that time he would have a GC) - and his L1 allows him to work as well as travel out and back into the country. One caveat though, since L1 and H1 are employer specific visas, unless you have an I765 approved, you will have to continue to work with your current employer.
Hope this helps for the starters... go on, get married, and worry about this after the honeymoon is over

lol. Best wishes.
USC