There are no subject requirements for law, and studying STEM subjects at A level would place you at no disadvantage. You would only be interviewed for a place to study law if you applied to and were shortlisted by either Oxford or Cambridge. If you apply to read law at either of those universities and some others including UCL, LSE, KCL, Bristol, and Durham you will need to take the LNAT, a test of your critical reasoning skills.
The main super-curricular activity to consider is reading about the law in general, and perhaps taking part in debating and similar activities. You are not expected to obtain work experience, although if you could find any there would be no harm in doing so. Court hearings are usually open to the public, so maybe visit a criminal and a civil court.
Obvious reading suggestions include The Rule of Law by Tom Bingham, one of the greatest judges of the last fifty years (sadly now dead), and Letters to a Law Student by Nick McBride, who is a Cambridge Law Don.
Why do you wish to study law? It's worth thinking carefully through the pros and cons of this.
I add that, if you are thinking of becoming a lawyer, that isn't an easy career option for a shy or anxious person, although it may be that your shyness and anxiety will reduce as you get older.