I do not think you will need to submit your HS transcript/grades at most UK universities, with the exception of Univ of St Andrews.
My feeling is that AP courses should be the ones of greatest interest to you amongst the choices available. If you want to study Classics or Ancient History, then you probably already are most interested in humanities area AP courses. Many are probably fine, depending on what your school offers. I would suggest taking, if you can, AP Art History, AP European History, and AP Literature, in addition to your AP Italian (which I think is a fine choice) but there are probably others that would work, too. IMO, it wouldn’t hurt to have a couple more, but other APs you end up taking could be in unrelated areas.
I don’t think having unrelated scores, such as an AP Chemistry score, hurt your application, but if you didn’t rely mostly on humanities scores when applying for a humanities course, that might be odd or problematic.