If you're drawn to Buk I cannot highly enough recommend the anthology "Hold-Outs". It can be a little expensive, but it has such a wealth of knowledge.
Or definitely Charles Harper Webb. He is easy to find online, also from Long Beach and he's really funny.
You guys would probably find Hold-Outs: The Los Angeles Poetry Renaissance, 1948-1992 interesting. LA poetry is its own beast and the book is very enlightening.
Bukowski's alright, his lines are a bit slack/loose for me, but he's not terrible.
He's not like Rupi Kaur, a couple older versions of her would be Mattie Stepanek or Ogden Nash. He's got a kinda bad name for a few reasons, the questionable (assholish) notions often espoused by the first person narrator which is compounded by the autobiographical nature of his work, but also he was notorious for not editing his work. So not only was he producing a ton, he was kind of 'first thought best thought'-ing them, and he didn't go through publications unless solicited (iirc), but a friend who had a press printed his massive books. Which results in a sort of watered-down body of work, whereas if he was doing more peer-review (publishing in journals) or honing his pieces a little more there would be a bigger academic support.
Of course, there is some support, especially in the LA area where his memory is alive and well. You can read about Bukowski and his contemporaries in the LA poetry scene in Dr. William Mohr's awesome book Holdouts: The LA Poetry Renaissance 1948-1992.
If you like Bukowski's accessibility you'll dig people like Charles Harper Webb, Gerald Locklin, Billy Collins, Denise Duhamel, Steve Kowit, Nick Flynn, Nick Lantz, David Kirby, Albert Goldbarth, Tony Hoagland etc., maybe even Bob Hicok... They're a rough 'school' of poets with a dozen names including "Ultra Talk" and "Stand-Up Poetry". I'd definitely recommend Charles Harper Webb's anthology Stand Up Poetry: An Expanded Anthology. There's a used copy on Amazon for $1.30. I believe there are a few Buk poems in there, but also a bunch of others who are still accessible, but a little more crafted.
Vuong is definitely more on the lyric/paratactic side, not nearly as far out there as they get, but it' not half-fleshed, it just takes a little practice/teaching to learn to read it effectively, but once you do it opens up a whole world of non-narrative/non-linear work. Parataxis, it's a good thing to get a handle on when reading modern (lower case modern) poetry.