Any Kurosawa movie is good. Hidden Fortress on the basis of its Star Wars influences (GL used it again for TPM) and Yojimbo for its influence on For a Few Dollars More (or is it Fistful of Dollars? I always get them muddled up) are the easy choices.
But I think Sanjuro has a lot to offer and High And Low is good too.
Continuing the classics theme, I'd suggest Spartacus - a Kubrick film like no other.
Rashomon and SS are my go to favorites but I like Ran, Yojimbo and Throne of Blood quite a bit. Also some of his earlier, non Samurai stuff is great too. Sanshiro Sugata, Shubun, and No Regrets for Our Youth, which in and of itself is a forgotten little gem, hold up quite well.
I personally never got much into Spagetti Westerns, as I always learned more towards Peckinpah than Sergio Leone, (although Once Upon a Time in America is one of my favorite films of all time with the single saddest post production hack job, ever). I see the value in them.
For Kubrick it makes perfect sense for our next one to be Dr. Strangelove since we all, well, love it. But I would totally be down for The Shining, as well. It goes without saying that as a DiF reservist I suggest movies at the leisure of the main four.