Every Oxford student is a member of one of its Colleges. Your college will offer you a great deal, and can play an important role in many aspects of your life, in - for instance - accommodation, pastoral support, travel funding, a stimulating cosmopolitan environment, social facilities of many different kinds, and further academic contacts in your subject and related areas: but it is important to be aware that, as a graduate, you will be doing work which is supervised and administered by the Faculty, so that the essential part of your academic experience here will be the same whichever college you go to.
Even though you must eventually be a member of one, you really do not need to choose a college at the application stage. We make offers every year to people who specify no preference in this matter, and those candidates are assigned a college by the system at a later stage. Not specifying a college choice affects your application not at all.
Among the main criteria used by applicants who do want to express a preference are: size, number of graduates, cosmopolitanism, beauty, location, history, atmosphere, facilities; and all these can be gauged - to an extent - from each college’s own website (if there is an Alternative website, that may be helpful too). It is essential to be aware from the start, though, that you'll be happy in whichever College you eventually find yourself - they all have many merits! It is however worth reflecting on whether you want to be at a college with both undergraduates and graduates, or one which caters exclusively for graduates.
It may also be worth enquiring whether there are at least two ancient world Fellows. 15 of the colleges which take both graduates and undergraduates have both a Literature and an Ancient History tutor: they are Balliol, Brasenose, Christ Church, Corpus Christi, Lady Margaret Hall, Magdalen, Merton, New, Oriel, Queen’s, St Hilda’s, St John’s, University, Wadham, Worcester). The colleges (Brasenose and New) where the two Ancient History Professors are based particularly tend to attract graduate applicants in this subject. In addition, Exeter, Jesus, St Anne’s, St Hugh’s, and Trinity have Languages and Literature Fellows; these all also have close formal links to ancient historians based in other colleges. Keble and Lincoln have Classical archaeologists, and Wolfson (which is a graduate-only college) has a large group of experts in Classical archaeology, linguistics, and many aspects of ancient west Asia.
Some candidates, having identified a potential supervisor, apply to the college where that scholar is based, and that is a perfectly reasonable strategy. But you should not feel bound to do this. There is also something to be said, indeed, for being in a different college, so that you gain a college advisor who is interested in your subject but who is not your supervisor. But since you can't predict for certain who will be available to supervise you, this calculation is not worth agonising over.