I'm the farthest thing from being a Kurosawa expert, but I'll at least echo most or even all of the sentiments of what has been said here.
I think that Seven Samurai and The Hidden Fortress are excellent starts into watching Akira Kurosawa. They can be simply enjoyed as action and adventure films, and still be appreciated for its technical and cinematic brilliance.
After having watched those films, delve into the his two other "Western" flicks: Yojimbo and Sanjuro.
After taking Akira Kurosawa 101, you can start delving into his deeper films such as Rashomon and Ikiru. Admittedly, I've never seen Ikiru, but I've gotten the gist from watching Madadayo how Kurosawa views life and death.
One point I'd like to make regarding Seven Samurai: it's every bit as great a movie as its reputation suggests. It's also one of the LONGEST movies ever made (3-1/2 hours? Something in that neighborhood). So any Kurosawa newbie that wants to check it out should make sure to take the steps necessary to watch a movie of that length. Get really comfortable cushions to sit on while you watch it. I've known a few people who tried to jump into watching Seven Samurai like any other movie, not being prepared for the length, and ended up just being outlasted by the movie
Seth, I'll have to watch the two scenes back-to-back someday. I had never really noticed any similarity before. The person I discussed this with a few years back tried to claim that ANH was practically a shot-by-shot remake of THF, and even had some examples to "prove" it. He even claimed that THF had a young farm boy and a older samurai master hiring a brash, younger samurai to help them rescue the princess.