Here is my problem...My daughter is 18 and we are trying to figure the best way to make sure she can stay with us as long as possible (best case would be a 1 year visitor visa). Anyway my question is would it be best for her to travel back and forth on a passport and then apply for a visa?
Since she is 18 now, the only way for her to actually live in the UK would be for her to qualify for a visa in her own right, for example, a student visa to study for a degree in the UK.
A 1-year visitor visa would not allow her to stay in the UK for 1 year, it is simply a multiple-entry visa for people who make frequent, short visits to the UK and who have a long, established history of visits over a number of years... for example, for academic conferences or regular business meetings.
Even with a 1-year visitor visa, you can only visit for a maximum of 6 months at a time, and it's very difficult to qualify for unless you can show an established history of visits to the UK over several years and a valid reason for needing to travel to the UK so often.
If she came as a visitor, she would most likely only be able to get a regular 6-month visitor visa, and would have to be able to prove that she has no intention of living in the UK and that she has a home and a life to return to in the US. I would advise applying for one before travel, since her family will be living in the UK and it may look like she's trying to use a visitor visa to live in the UK illegally.
There is a chance when we go in May for her to find a university that suits her. In that case i'm guessing it is best to apply for a student visa? So many questions.
As she is only 18, a student visa would probably be the best option, though she would need to look into entry requirements for UK degree programmes to see if she would be accepted (she would likely need AP or college-level classes to get accepted to an undergraduate degree).
She also needs A LOT of money available to her in order to qualify for the visa, either in her bank account in full or by way of an approved US loan (i.e. FAFSA or Sallie Mae) - she would need 1 year of tuition plus 9 months of living costs available to her.
International tuition is about £15,000 per year (depending on course) and the required living expenses for studying outside Inner London are £9,135 (and for studying in Inner London are £11,385).