marrying in the us to us citizen

i have met a wonderful american woman i wish to marry ,im a uk citizen and am new to immigration ,would it be possible to go to the states on a longish holiday and marry her whilst there , my aim is to live with her there as she has young children ,im looking for a way to stay and work eventually but obviously i would want to stay there as long as possible ,or would it be better for her to marry me here ,im looking for a straightforward way ,im concerned as i am a student who has been a carer for a partner for the past 8 yrs and has no real income records ,though i intend on working whilst in the states ,i would appreciate any advice ,thanks in advance to anyone who could help ..