Children (though your girls are a bit old to be called 'children') like strong rhymes and rhythms and often pick up verses by heart after hearing them only a few times. Sad love-poems are popular - like Poe's 'Annabel Lee' which I used to weep over and which ends (rather gruesomely, as is Poe's wont)

'So all the night tide I lie down by the side
'Of my darling, my darling, my life and my bride
'In her sepulchre by the sea,
'In her tomb by the sounding sea'

Then there are ballads - 4-lined stanzas with regular rhyme-scheme, usually telling a story - like 'Lord Ullin's Daughter'

These are the regular things. But they may like 'free verse' with no regular rhyme or apparent pattern - choose some which are easy to understand.

There must be lots of good poetry anthologies on sale these days, with poems from all ages and by all kinds of different poets. have a look in a good bookshop and choose something which is interetingly presented, possibly illustrated, as well as varied in its choice of works.

Dido

One anthology that might fit your bill is The Rattle Bag edited by the poets Ted Hughes and Seamus Heaney.
I haven't read it but understand it is aimed at children/young people and has a wide selection of good quality works.
I think it is now out of print but there are quite a few copies for sale via the Amazon sites in both the US and the UK.
I think the way to encourage children to enjoy poetry is initially to read it with them, rather than to make them sit and read it to themselves . . . which they can do later.
I remember as a child we were read poetry at school. We never saw it written in a book (of which only the teacher had a copy) and surprisingly we subconsciously 'took in' quite a bit of it and I can still recite some today. ;-)

I've got the Rattle Bag - it's very good. Made a stir when it first came out and rightly so.

It was my father who first got me into poetry. He was an english teacher and he used to sit by the fire of an evening and recite whatever he felt like. I remember Wordsworth's 'Lucy', and Hardy's 'In the time of the breaking of nations'. And he always had one particular line which he reckoned was the best:

'And oh, the difference to me'
(Lucy)

and

'With an old horse that stumbles and nods,
'Half-asleep as they stalk.'
(Hardy)

And he would comment on one word:

'difference', from the first - such an awkward word but so right in its context. And:

'Stalk'

in the Hardy.

I was talking to the Lakes poet Norman Nicholson (now deceased), a few years ago, and I asked him what his favourit line was. He said, it was from Wordsworth's 'MICHAEL' - about a father and son in a pact to build a drystone wall, but the son reneges and leaves the area. His line was:

'And never lifted up a single stone'

I often ponder that. It's not such a great line, as it stands, out of context. But it has a good rhythm and shape, and it's enigmatic. I think mine might be:

'I stood in Venice, on the Bridge of Sighs'
(Byron)

Again - shape. And it fires the imagination. I've still never been to Venice; and the 'Bridge of Sighs', though I know it's real, could still be a metaphor.

Dido

I review children's books for a local newspaper, and I came across this title which might work. It's a UK book, but easily available on-line and elsewhere. I like that the poems are chosen by the kids for the kids... Nice touch, I thought. Here is the relevant part of the review... Perhaps this might help.

I Like This Poem -- Kaye Webb

A collection of poems (both old and new) that have been chosen by children for other children just because the kids liked them. Although this is a British book (and with an emphasis on British poets), kids will come across familiar poems and perhaps be introduced to new ones. The poems are grouped by the age of the kids who chose them, and who range from six years old to 15 or so. An extra nice touch is that each poem has a footnote saying just why each kid chose that particular poem -- makes it very relatable to the young reader, I think. A fun way to introduce younger readers to the word play of poetry, this anthology is wide enough for almost everyone to find a favorite poem. ItâÂÂs a good example of how fun language and words can be as you get comfortable with reading. (Super fun to read aloud as well.)

liz/lemonhead Kaye Webb did some marvellous work for children in her role as editor of Puffin books, the arm of Penguin that produced books for young people. Many years ago she introduced the in-house magazine 'Puffin Post' (now long gone . . . which encouraged kids to write their own stories, enter competitions etc). You probably know she was married to talented artist and cartoonist Ronald Searle, famous for his St Trinian school-girl sketches/films.

Here is a link that might be useful: St Trinian's School

Thank you for the many applicable suggestions. Sadly, no one read to me when I was a youngster but, with my own children grown, I delight now in reading to my great grandchildren, attempting always to portray voices as did The Singing Lady to whom I listened by radio many years ago. I will never forget her, and feel she lead me down the amazingly rewarding path of books and poetry.

I m surprised no one has mentioned "Silver Pennies" an anthology compiled by Blanche Jennings Thompson. Many well known authors and memorable verses that children would enjoy. I remembered it from my childhood, read it to my daughter and her children loved it.
Available from Amazon.com