Here are my favourites:
Philip Larkin -- one of the greatest English poets, who uses the English language in its most elegant, plain and beautiful way. Often deals with death and love. A sample poem about the fear of death
Derek Walcott -- A poet of the Caribbean, known for epic poems. A sample poem about love
ee cummings -- a popular American poet who played with form. A sample poem
Emily Dickinson - maybe one of the most famous American poets, you can read a lot of her poetry online
Also online are the other big famous poets: Robert Frost, Langston Hughes, Maya Angelou, W.B. Yeats, Walt Whitman, Keats, William Blake, Anne Sexton, Sylvia Plath, John Ashbery. For each of these I'd just suggest googling and seeing what you like.
But I'm going to suggest to you some poetry by some new, rising poets, who are still alive and writing.
Sam Sax -- a young queer American poet who was the winner of the National Poetry Series. His work is incredible. Here is a video of him performing one of his earlier poems
Meg Freitag -- another young American poet who writes intimately about the self, heartache, etc, with gorgeous imagery. A sample poem
Kaveh Akbar -- an Iranian-American poet who has won a ton of awards.
Claudia Rankine is not young or up-and-coming given that she won a MacArthur and a Pulitzer prize but she is one of the most important poets writing today, and her work often revolves around blackness in America. She also writes prose poetry.
Maggie Nelson is also already famous -- Bluets is the most beautiful book, a meditation of grief and the colour blue.
I would honestly just go browse through https://www.poetryfoundation.org. It's so fun, and you can read poets by theme. That's a very good way to get into both classical and contemporary English language poetry.
If we're talking whole-career unimpeachability; Boards of Canada and Godspeed You! Black Emperor. (Even Radiohead had Pablo Honey, right?)
Books... The Crow Road, Iain Banks. Collected poetry of Philip Larkin (total bastard but brilliant poet); check out Aubade. And, of course, Animal Farm by George Orwell...