Spouse Visa Settlement / Student Visa implications of trying

Hi im a desperate for some help / advice after going to solicitors and visa specialists regarding my girlfriend

I was born in the uk and have always had a job since leaving school at 16 , no problems with me except very nervous about marriage

girlfriend is american and has been here (overstyed) for 3 years , her mother (has residency but not citizenship) tried to use the exceptional circumstances try to keep her daughter in the country as she was poorly advised ( this was VERY wrong) - since then we have NOT applied for anything but were hoping for the unmarried partners visa - which we have been told NOT to do

so this leaves us with Student visa or marriage - but ive read that these are 2 very different forms of visa - marriage is settlement and the overtaying could be almost ignored , where as with the student visa it may not bee ignored

SO - do we have no option but to get married or can we try for the student visa ( with the honest intention of getting her on a good college / uni course and then seeing how we feel about each other at the end of that course or courses)
BUT if that is rejected , can we get married in america and apply for spouse visa with no worries about her past immigration history ( and the very obvious fact that she would have JUST been refused a Student visa)

we have been living together for the past 2 years but have little evidence to prove this - as we have been a little short on cash , we havnt been anywhere to take photos etc - but LOADS of people to write and swear the relationship exists - plus we live RIGHT next door to my parents house

Any help or advice would be sooo welcome !