THe whole set? Wow, that would be a lot of money! I've never heard the Alban Berg recordings but I've heard good things about them. I never had the nerve to buy the whole set but I've picked up individual box sets of different stages. Since I never got into the early string quartets I never got a recording of them bu tthe Tokyo String quartet had a recording of those I listened to and enjoyed. I'm more into the late quartets. Reissues can be a good way to go. I have a reissue of the Busch quatet recordings from the 1930s. The sound quality, naturally, is not awesome but the performances are compelling. I also have the Emerson string quartet's recording of the late quartets and have enjoyed their take on the works. For the middle quartets there was an interesting reissue of Library of Congress recordings of the Budapest quartet that pretty quickly won me over.
I know you're asking about all the Beethoven string quartets so I don't want to discourage you from getting a single box set of those but I also want to let you know that finding a single ensemble that nails everyone of the quartets might be tough to find and even if not that, it might be tough on your checkbook.
If someone has a recommendation for an ensemble that tackles the whole set I'm interested in reading about that, too.