For a long time Edgar Allan Poe was my favorite poet. His poems are so
melodic: when I read them aloud I often sing them as a song! He makes use of meter, rhyme, alliteration, etc. His subject matter — often his yearning for a dead mistress — appealed to my own nostalgia and bouts of gloom. I also love Poe's essays on poetry. Read "The Philosophy of Composition" in which he practically proves that "The Raven," in all its detail, is the inevitable result of a quest for writing a perfect poem!
I liked Poe so much that I was annoyed by the large majority who insist Robert Frost is the greatest American poet. But I've matured somewhat and now realize they are probably correct. Frost's poems have deep heart-moving messages, but even their more superficial aspects, like rhyme, are exquisite. The AABA/BBCB/CCDC/DDDD rhyme pattern of "Stopping by woods" is special (and unique?) but look at his less well-known
"The Gum Gatherer". It almost reads like prose rather than poetry. But it does have a rhythm, albeit haphazard, and the line-ending words do rhyme, although in a haphazard fashion. The net effect is to turn a dullish story into a pleasant read.
I've occasionally dabbled in writing poetry myself: e.g. a villanelle about Donald Trump, and a line-palindrome in response to 2001-2003 terrorism; but you should be happy to know I do not intend to inflict these efforts on you.