For KCL, Manchester, Edi & UCL if you have the entry requirements and a decent LoR & PS you should get an offer. Being an American is a strong positive, as you bring those nice $$ with you…
St Andrews considers GPA more than most UK unis, and is a little bit more holistic than average. On the other hand, classics is not a typically one of their most over-subscribed courses, so if you meet the requirements I would fancy your odds.
You can only apply to one of Oxford or Cambridge. fwiw, Cambridge has a rep for being cooler on US applicants than Oxford. Both have an aptitude assessment- Cambridge at interview, Oxford as part of the interview selection process. There is really no way to handicap Oxbridge admissions- the entry requirements just qualify you ,and the aptitude test is critical to getting the interview, but in the end a lot of it comes down to the interview.