Steve Martin's stand-up is brilliant. So whacky and surreal. He was probably amongst the first comics I came across when I first discovered it, along with Bill Cosby and Billy Connolly. His first ever TV appearance was on The Smothers Brothers Comedy hour, which came up as a recommendation when I watched that other clip you posted, which I'd never seen before.

I'm familiar with Andy Kaufman, but haven't seen much of his stuff.

I also recommend Maria Bamford (US) and Stewart Lee (UK).