Your english seems very good, make sure it's up to scratch as much as you can, pretty much blanket statement to any international, especiallly for language courses. I know my room mate is slowed down in his work, he's German and studying Persian and quite often has to mentally translate into german first, naturally the better your english the less you will need to do this.
Language is a big part of classics at Oxford. If you have the equivalent of A level latin you will have one latin class a week, and then daily greek classes. It is most likely that should you get a place you will be asked to attend a summer school or self learn to the equivalent place the summer before you come up.
I would suggest exploring greek, find out if you could study it for 4 years. If you come in with good latin then you will have no choice but to study greek at least up to mods, and it is a hard language (currently pulling my hair out over it). If you can get some tuition or look through the JACT reading greek course, as thats what will be used. Also look at enrolling in the JACT summer schools over here or look for Italian equivalents.
With classics its such a broad area, read whatever interests you. Preferably in the original if you can, also maybe some literary criticism. Generally I think a tutor would find it a little odd if you hadn't looked at either homer or virgil, and then I would suggest looking at stuff of the beaten track: art history; archaeology; Love poetry; history; philosophy (modern or ancient, one of my interviews digressed into a talk on nietzsche)
Basically I would suggest working on language skills, showing an interest in the subject via reading. Expsing yourself to classical languages as much as possible and also doing the best you can at school.