The best edition to use is the multi-volume Twickenham edition, general editor John Butt et al., and for the purposes of Honours, the one-volume edition, edited by Butt, will contain everything you need.
Everyone who writes on Pope in Finals will write about The Rape of the Lock, so try to have something else to say as well. (In any case, you might look at the very first, two-book version of the poem, for which you will need to consult the separate Rape of the Lock volume, edited by Geoffrey Tillotson, in the Twickenham edition: thinking about what Pope added – the ‘machinery’, and then Clarissa’s speech in Book V – is the heart of a very good discussion of the poem.)
Other poems: The Dunciad, especially books I and IV; Essay on Man (read it with the Nuttall book, below); the Moral Essays, especially ‘To a Lady. Of the Characters of Women’ and ‘To Burlington. On the Use of Riches’; ‘Epistle to Dr Arbuthnot’; ‘Eloisa to Abelard’. Of the prose, the ‘Preface’ to Shakespeare is interesting, as are the remarks on translating Homer.
A succinct list of secondary reading.
(i) Pope in particular.
Howard Erskine-Hill, Pope: The Dunciad (1972)
David Fairer, Pope’s Imagination (Manchester U.P., 1984).
-- ‘Imagination in The Rape of the Lock’, in Essays in Criticism 29 (1979), 53-74.
Jones, ‘Pope and Dullness’, in Proceedings
of the British Academy 54 (1968), 231-63.
A.D. Nuttall, Pope’s ‘Essay on Man’ (1984)
Pat Rogers, An Introduction to Pope (Methuen 1975).
Felicity Rosslyn, ‘Deliberate Disenchantment: Swift and Pope on the Subject of Women’, in The Cambridge Quarterly 23 (1994), 293-302.
(ii) Mock-epic, satire, epic, eighteenth century poetic language.
Ian Jack, Augustan Satire: Intention and Idiom in English Poetry, 1660-1750 (1952, etc.)
James Sutherland, A Preface to Eighteenth Century Poetry (1948, etc.)
Geoffrey Tillotson, Augustan Poetic Diction (1964).