The British Library website and The Victorian Web are good places to start your background reading on Victorian Verse.
Start here: Victorian Poetry and Victorian Literature
You need to know something about the two, long Tennyson poems from which you are required to study extracts - In Memoriam AHH and Maud. The extracts work as stand-alone poems, but the context is important. A useful introduction to Tennyson can be found here.
I would strongly suggest that to understand Tennyson, and appreciate how good he is, you should read two of his shorter, and possibly greatest, poems - Ulysses and Tithonus. Both are in the anthology. Why they have been omitted from the selection I have no idea, except it suggests an effort to thematically link all the poems in the selection with each other.
There is a Browning society whose website is here
Here is information on Elizabeth Barrett Browning's: Sonnets from the Portugese
Elizabeth and Robert Browning were married. It was a famous love affair as they had to elope: Elizabeth and Robert's marriage
There is extensive information on Robert Browning on the Victorian Web. You should read some of his other dramatic monologues to understand his mastery of this form: Porphyria's Lover and The Laboratory.
Here is information on Christina Rossetti. You might want to read "Goblin Market" which is probably her most famous poem. It will shed light on the other poems. There is a critique of it on the BL website here which is also useful for understanding something about her poetic form.
Art and Literature in the Victorian age are closely linked. "Goblin Market" was illustrated by Christina's brother Dante Gabriel Rossetti, a famous pre-Raphaelite painter, and she also sat as his model: Ecce Ancilla Domini (Behold the Handmaiden of the Lord). Here she is shown as the Virgin Mary hearing that she is to bear Christ.
Thomas Hardy is a very different writer. Although born in 1840, he lived until 1928 and feels more "modern" than the other poets in this collection. He is probably best known as a writer of novels,such as "Far from the Madding Crowd " (1874) and "Tess of the D'Ubervilles" (1891) set in the legendary county of Wessex (modern Dorset/Hampshire) which deal with the lives of the rural poor in an England which had become increasingly urbanised and mechanised.
Hardy was also a social reformer. Here is an interesting article: "You ain't ruined" which looks at Hardy's response to the Victorian (and modern?) link between sexual purity and moral virtue.
Further details on Hardy on the Victorian web.
