I applied direct to the uni as I was a mature student so didn't need a PS, but I had done an Alevel on Classical Civilisation. But it doesn't matter, you studied Classics. Talk about your love of Homer, or how you want to understand their daily lives, or the gods , or even just their military tactics. You've picked this degree for a reason, you don't need to show off knowledge, you just need to show your love of the subject.
Good choices! Look at the modules and then the staff, see if any of the staff work on anything that interests you - Classics departments tend to be quite small so you'll work with the staff a lot, particularly in 3rd year when you do a dissertation, so make sure there is enough staff that have similar interests as you. 2 unis by me offer Ancient History, yet as my interest is in Greece, the one with mainly Roman modules wasn't going to be as good for me.
If you haven't looked already I'd recommend my own uni - Swansea University. It's a small department with great staff and modules, including Egyptology (and we have an Egyptian museum on campus), and the city and campus is right on the beach. Its a good uni and the staff are brilliant, including the Student Welfare side of things. The department even holds film nights for staff and students - we watched The Mummy and Hercules (Disney, yay) last year.
Book wise, the Stephen Fey series Heroes and Mythos is really good, he's definitely brought the ancient gods and stories more mainstream and he references everything in his usual funny style, even my lecturers have read them and approved. Even playing the Assassin's Creeds games, while not fully accurate, really brings some things to life, and we've discussed them in class. Things like Homer, Ovid, Plutarch will come up in your degree, so you if you wanted a headstart or just to read over the summer they are a good choice (and cheap).
If you have an interest in Latin or Ancient Greek,
https://www.bloomsbury.com/cw/latin-to-gcse-parts-1-and-2/ This series of workbooks is great. They offer both Greek and Latin to help you do a GCSE and up, and they are pretty cheap. It's the workbook my uni uses for teaching (as usually there will be different classes depending on your level with the language: beginner - no Latin, intermediate - done a gcse/low Alevel, advanced - Alevel and expert.) I've never studied Latin and I've found the workbooks great and really in depth yet simple, with lots of questions and tasks. Since your summer will be spent indoors now, maybe worth trying to learn one of them, even if you don't end up taking a language as a module, it's still fun to learn and see how our words are shaped by theirs.
Anytime! I really believe and love this subject and would love to see the subject grow and for more people to study it. The amount of times I've told someone my degree and they say 'wow. I love XYZ' and then add 'useless degree though' is annoying. Who do they think runs museums, or helps movies stay accurate or teaches their children?! Hopefully me answering your questions helps you decide where and what you want to study, in which case that's great, go convince some friends now too! 🤣