The Waste Land is as good as any place to start with Eliot, though I would recommend The Love Song of J. Alfred Prufrock and The Hippopotamus.

Robert Browning is a great character poet. Look for his dramatic monologues, particularly
The Bishop Orders His Tomb at Saint Praxed's Church, My Last Duchess and Porphyria's Lover.

I'd also recommend looking out for Sylvia Plath, particularly Morning Song and Lady Lazarus; Philip Larkin's High Windows and Friday Night in the Royal Station Hotel; I'd even suggest you hunt out a collection of Nick Cave's lyrics.