I just find them all to be so obviously not him to the point where it just detracts from the whole experience. It's an attempt to emulate a aspect of his already existing stories where Lovecraft himself didn't go down that route. We all know he isn't the tentacle and sunken city guy, but the people emulating him seem to fail to grasp that. Tentacles and seas aren't what's scary about Lovecraft. The implications raised by the explanations of the mythologies, folklore and history is what's scary about Lovecraft.
Lovecraft really hit the imagination of fantasy/horror writers after him that a lot of his shit is tangled and mixed in with misconceptions.
That being said, he's still great fun.
I've personally found his stories to be lacking compared to the above two (static and archaic, probably purposefully, but that still doesn't fix it), while his worldbuilding, at least in concept, might have been better and more creative than them.
I think he's a fine read if you're in the mood for them. His prose is leagues better, but it can filter people out.
For the big Weird Tales writers, Smith's usually considered the heavyweight in terms of sheer prosaic skill. The man was more of a poet than storyteller. I'd have to say Robert E. Howard is my favorite of the "big three" of Weird Tales (Howard, Smith, Lovecraft).
I will say, picking any writer that made their bones in that pulp magazine isn't bad. Manly Wade Wellman is fun and I really liked Silver John. Seabury Quinn's Jules de Grandin stuff isn't rocking the world, but they're fun little occult detective tales. August Derleth, Carl Jacobi, Frank Belknap Long, Donald/Howard Wandrei were all solidly enjoyable writers that were known for contributing to the Cthulhu Mythos and were older members of the Lovecraft Circle. Then you got to the likes of Robert Bloch, Ray Bradbury, Tennessee Williams, Henry Kuttner, C. L. Moore, Edmond Hamilton, and Fritz Leiber who all went on to greater pastures. They're all enjoyable. Williams had a fun story about Nitocris (Ancient Egyptian figure of some sort). It was one of his first! Bloch's penchant for horror was sharpened in the '30s. I haven't read "Psycho" yet, but the Hitchcock adaptation was great.
Bradbury and Leiber got their horror start with Weird Tales. Fun authors. Bradbury needs no introduction, man was one of the most prominent American fiction writers of his era. Leiber created Fafhrd & The Grey Mouser and was a major cog in the development of modern fantasy and DnD. He also did great horror. Leiber and Bloch were both part of Lovecraft's circle and he did mentor them. I think Bradbury came on the scene too late to be mentored by Lovecraft. You can easily find their horror work, it's been collected very often.
Edmond Hamilton got his beginnings in Weird Tales. He was one of those early pulp era SF pioneers that branched off and heavily influenced early modern SF and Space Opera. His Weird Tales days also probably influenced a lot of his later comics output with the weird science sorta stories he'd pump out in the '40s-60s. Solid writer, I remember "What’s It Like Out There?" as a memorable tale and rather seriously introspective relative to the time it was published. He's largely slept on these days and it's a damned shame. He was married to Leigh Brackett and they certainly influenced each other. (Brackett was a female pulp SF writer and Hollywood scriptwriter who worked on The Big Sleep, Hatari, and The Empire Strikes Back. She's a fun writer to read and has lots of good work. )
C. L. Moore was a woman writer. She created Jirel of Joiry, the first female sword and sorcery protagonist and also the first one to be written by a woman. She also created Northwest Smith, a proto- Han Solo style character. She got congratulated by Lovecraft for her debut work and may have been a late member of the Lovecraft Circle (don't remember). Moore was an excellent writer and eventually married Henry Kuttner, another pulp writer. When Kuttner passed away in '58, Moore never wrote SF/F again. Moore and Kuttner worked together a lot, so it's hard to tell who did what on their works after they got married. Kuttner was called a "Neglected Master" by Ray Bradbury and never quite wrote a definitive novel. He's still a splendid writer who has a knack for worldbuilding and imagery. Moore and Kuttner worked together on many stories, like "Mimsy were the Borogroves" and "Two Handed Engine". I know there's a LOT of collections that have their work together or individually. I could sperg more, but I think their work holds up well. It's widely available second-hand, on kindle, or on specialty presses like Haffner Press or Subterranean Press.
Weird Tales is apparently on its third or fourth iteration as the "Magazine that never dies". Nowadays it's edited by Marvin Kaye and. . . apparently got criticized for having weaker stories. Marvin Kaye's gotte be an octogenerian at this point so I guess he's a figurehead.
As for other great semi-forgotten SF/F writers, I just don't hear enough people talking about how fun Cyril M. Kornbluth was in his short fiction. Man also died young. . . in 1958. But he was a fun satirist and a hell of a weirdo. His best buddy and frequent co-author, Frederick Pohl, went on to have one of the longest careers in SF and wound up being pretty widely respected. Their crowning piece they wrote together is probably The Space Merchants. I keep getting told to read it, and will do so later this year.
Another fun one that's also not talked about often is Robert F. Young, a guy who wrote SF in the 50s-60s for magazines and was compared to Ray Bradbury. He apparently had a lifelong career as a school janitor and died unknown. Shame, because his work's really well written and rather poignant.