There are some subjects that are just obviously better to study in the UK, particularly Medicine and Law, which can only be read as postgraduate courses in the US.
However, for many students, even knowing what you want to study is not necessarily sufficient. I went to university knowing exactly what I wanted to study. I was president of my secondary school's math club; I convened the school's week-long math-fest; I asked for International Mathematical Olympiad problem books for Christmas presents (I was truly that sad). I knew that I wanted to go to study to read PURE MATHEMATICS. Ahhh... the folly of youth. This lasted until I took my first pure mathematics course (Analysis I). We started the course spending two weeks and eight pages of Greek letters proving the existence of the rational numbers (fractions). Now this bothered me a little bit. From the time DD was age 2, I could say things like "You may eat half of that biscuit", and she understood. I wasn't completely convinced that it was a good use of my time to be spending 8 pages of Greek letters proving the existance of something that I accepted as a primitive at age 2. I realised then, what I still believe today, that while I am really glad that there are pure mathematicians out there, pure maths is too much mental masturbation for me to feel comfortable making it my life's work, and I needed something more real but which still utilised my love of maths in order to be happy. Now I was lucky. If I was at most UK institutions and realised 2 weeks in that I had made a terrible mistake, then my options would be to suck it up and get out with a degree vaguely related to what I enjoyed, or to withdraw and then to reapply the following year for a different course. But I was at a US institution where changing majors was trivial.
One advantage of the American approach (at most institutions) is that it does give you the chance to experiment. You may come to university loving Chemistry, but do you know whether you want to major in Chemistry, in Materials Science/Materials Engineering (which is basically inorganic chemistry), or in Chemical Engineering? Do you really know the differences between these at age 17. I did not. This is not including all of the subjects (e.g. Archaeology, Sociology, etc.) that you really never got to try in secondary school.
As to the logistics: Many UK institutions do not know anything about US applications. It can be difficult to get useful unbiased answers about the process and about selecting institutions. A good independent source is the Fulbright Commission, founded by diplomatic treaty in 1948, to foster intercultural understanding between the US and UK through educational exchange. They have an independent non-profit advising service (
http://www.fulbright.org.uk/going-to-th ... ergraduate).
The SAT as you note mostly covers GCSE level maths (and the equivalent English). I would recommend getting it out of the way as soon as possible (year 11 or latest year 12) if DD knows she wants to study in the US. Be aware that there are some differences in curriculuum in the SAT II subject tests. For example the SAT II Physics test covers an introduction to general and special relativity, which does not appear in most UK curriculuums.
As to money, if you can get into one of the top US institutions, it will probably be cheaper than most UK institutions. Note that this probably only applies to the top schools. Princeton was the best of the schools last year. 76% of the class that graduated in 2016 finished with no school debt. The average debt for the 24% who had debt was some USD$5000 (around £3500). For Harvard, it was about 66% and some $18000 in debt (£13.3K). There is a key differential between the questions "What does it cost?" and "What will I have to pay?" as the sticker price is very high, but only the very wealthy pay it. The exact aid package will differ between schools, but as a rule of thumb, if the family income is less than around £55K, then tuiton will be free. If above £250K, then tuition will be full price and everything in the middle is a sliding scale.
You ask if there is a way for students to know roughly how much it will cost prior to application. On the website of any school that takes US government money (which is basically all of them), they have to have somewhere a tool called the "net price calculator". It should be easy to find on the financial aid pages (and if it is not then that is often a bad sign). The NPC takes some broad information (family income, any trust funds lying around) and spits out a rough estimate of costs. It is a crude instrument. You might have a large income but 3 children in independent schools, and hence no available disposable income. The full financial aid application will tease this out, the NPC will not, but it should give you a decent picture of likely costs. The full financial application can be completed at any time, but I would recommend completing it immediately after you complete the admissions application. You want the admissions decision and financial aid award to arrive at the same time, so you can make comparisons (DD could go to institution 1 which would cost this much or perhaps to instution 2 which offers this much aid) before making a decision as to where to attend.
As to post-education employment, that really depends on where you go. If you apply to a job in the US with a degree from Cambridge, Imperial, LSE, or some other school that they have heard of, then that is a very good thing. If you apply with a degree from (say) the university of East London, then that is less valuable. It works the same in reverse. Applying to a UK employer with a Stanford, Yale, or MIT degree means a lot more than one from the University of Oshkosh. However, I have rarely seen a strong preference for a UK degree in hiring. Your university degree is really only important for your first job, and after that it is your skills and experience that moves you up the ranks. After that the only important bit is that you have a degree.
Good luck.
[Note: Edited but only to fix spelling errors]