If I want to read poems every now and then,would a textbook style anthology be a good buy?

Get A Book of Luminous Things by Czeslaw Milosz, and other anthologies like it.

Well, it depends on your taste. Getting anthologies from Milosz, Simic and others is a good place to start. There has been a massive amount of poetry written in that time period, and some of it is reminiscent of the older lyric styles, while others do away with form altogether and look at the line as an independent entity, which also has a tradition from the Deep Imagists like Merwin. Anthologies are a good place to start regardless, because the poetry community is so self-referential and inclusive it is hard to know why poets are doing what they are doing unless you have some background.

Milosz is a great poet in his own right, but he also introduced me to a lot of other poets. He's a good place to start if you are unfamiliar with modern poetry.

ETA: The Book of Luminous Things is also a slender volume, and Milosz sort of explains what he likes about each poem in plain language.

In addition to the Milosz book, I would recommend the Norton Anthology of Contemporary Poetry rather than the one you linked, which will have more older poets in it.

Are you a fan of any particular poets?

I think you have to figure out what time period you enjoy the most. Contemporary, Modern, or even older poetry.

I personally enjoy Walt Whitman (whom I really didn't "get" when I was 20) from an older period; a guy named Louis V. LeDoux from the last century; and a North Carolinian named Fred Chappell. If you can figure out what style you like, you could dive in. I generally don't read much poetry, but sort of like beer, when I find one I like I go for it when I want a beer.

Good luck!

This thread got me looking up poetry on youtube. Alec Guinness reading Wasteland is a work of art in itself.

I don't really understand the poem but that doesn't matter.

Youtube

Here is a list of poets, some old, some new, that you may find helpful. You can find most of these on Poets.org or the Pretty Foundation site. In no particular order, I've enjoyed the work of Wallace Stevens as well as...

Adam Zagajewski
Elizabeth Bishop
Mark Doty
Yusef Komunyakaa
Robert Lowell
T. S. Eliot
W. H. Auden
Alexander Pope
Sylvia Plath
Donald Hall
Seamus Heaney
Zbigniew Herbert
Anne Sexton
Robert Hass
David Bottoms
Robert Creeley
Pablo Neruda
Langston Hughes
Charles Simic
Jack Gilbert
Meghan O'Rourke
W. B. Yeats
Philip Larkin
Mary Oliver
Robert Frost
John Ashbery
Jane Kenyon

That's a good list, but it misses the post-2000 poets. And any list of 20th century American poets has to include James Tate, Galway Kinnell, WS Merwin, Ginsburg, James Merrill, James Wright, Gwendolyn Brooks, John Ashbury, John Berryman, and so many more I'm forgetting.

There are some incredibly wonderful poets who no one seems to recall. The Yale Younger Series is a great place to start for contemporary poets. Richard Siken's Crush is such a lovely book. Though people feel strongly about him, I love Terrence Hayes. There has been so much lovely work since 2000 that will never get the acclaim of the older, 20th century poets, which is sad.