First, second, third and fourth.....grades.
There are lots of things Universities will be looking for, but a good crop of GCSEs is both an important preparation for A level, but used as a selection tool for some med schools.
Fifth and six. The right A level choices. Read student room and relevant University websites. Some want two lab subjects, most want chemistry, not all want biology, and some won't consider double maths as 2 A levels etc. Then your daughter should match with her interests and abilities, again leaving as many doors open as possible.
Seventh...it is all an awful lot easier if you get good aptitude scores, so plan your summer holidays before yr13 around time for revision/practice. (UKCAT is a timed test so speed is of the essence.)
Eighth. Spreadsheets. Cut and paste a list of medical schools and then complete columns. What are they looking for? DD had strong academics but no BMAT and a poor UKCAT so that cut out quite a lot. She did, though have good shadowing and volunteering, which gave her an edge in a couple of places. Once we filtered out the ones who did not offer what she was looking for (city, possibility to intercalate etc) there were not many left. You can only apply to four anyway, so as long as you apply to your strengths, you really don't have to tick all the boxes.
Ninth..see it as a two year process. The main aim of Yr13 is to get the grades, as without them you won't be going anywhere, and plenty get places on reapplication.
Shadowing and volunteering are valuable, but as much for the student themselves. It is all too easy to get wrapped up in the process of applying to medical school without re-checking that this is what you actually want to do. (PP seems to be regretting it, and each year there will be several in each medical school trying to find exit routes.) DD spent a summer cleaning, waitressing and kitchen portering in a care home. She loved it, but was never asked about it at interview. However she knows now that she would be happy in geriatrics, whilst paediatrics - she worked for a family holiday company in her gap year, would probably be quite challenging. The more you know why you want medicine as a career the more enthusiastic/informed you are likely to be at interview.
And don't get worried about the state/private school thing. People make a big thing of it on MN. DD is at a University known for a high intake of affluent private school kids from the South East. The medical school demographic is very different. DD went to a private school but none of her close friends did and very few are from the South East. My theory, I could be wrong, is that the NHS wants to train a lot of GP's especially for hard to recruit areas, so want to recruit a good mix of students from across the country.