Read: the poems (Collected Poems, edited by Anthony Thwaite); and the two novels, Jill, and A Girl in Winter.
There are two different volumes calling themselves Larkin’s Collected Poems, which is confusing, and, worse, both are edited by Anthony Thwaite (both published by Faber). The 1988 text includes almost everything, on the whole arranged chronologically: look especially at pages 81–210 if you have this book. The advantage of the 2003 text is that it prints the poems in the order Larkin himself carefully arranged them, volume by volume: concentrate on pages 43-198 if you have this one.
And there are two important and illuminating volumes of Larkin’s criticism:
Philip Larkin, Required Writing: Miscellaneous Pieces, 1955-1982 (1983); and Further Requirements: Interviews, Broadcasts, Statements and Book Reviews (2nd edn., 2002).
John Bayley, * ‘Philip Larkin: The Last Romantic’; in his Selected Essays (1984).
— ‘Larkin and the Romantic Tradition’; in his The Order of Battle at Trafalgar and Other Essays (1987 ).
— Pages in The Uses of Division: Unity and Disharmony in Literature (1976).
John Carey, ‘The Two Philip Larkins’; in James Booth (ed.), New Larkins for Old: Critical Essays (2000).
Donald Davie, pages in Thomas Hardy and British Poetry (1973).
Barbara Everett, * ‘Philip Larkin: After Symbolism’, and ‘Larkin’s Edens’; in her Poets in their Time: Essays on English Poetry from Donne to Larkin (1986).
— ‘Art and Larkin’; in Dale Salwak (ed.), Philip Larkin: The Man and His Work (1989).
— ‘Larkin’s Money’; in James Booth (ed.), New Larkins for Old: Critical Essays (2000).
Raphael Ingelbien, ‘From Hardy to Yeats? Larkins's Poetry of Ageing’, Essays in Criticism 53 (2003), 262-77.
Clive James, ‘On His Wit’; in Anthony Thwaite (ed.), Larkin at Sixty (1982).
Laurence Lerner, Philip Larkin (1997).
Blake Morrison, The Movement: English Poetry and Fiction of the 1950s (1980).
Andrew Motion, * Philip Larkin: A Writer’s Life (1993).
Stephen Regan (ed.), Philip Larkin (New Casebooks; 1997).
Christopher Ricks, * ‘Like Something Almost Being Said’; in his The Force of Poetry (1984).