I'd buy the new Endellion String Quartet box set before the Italiano. The Endellions are more direct in their communication, whereas the Italiano are softer, less Beethoven the way I understand him. They also use the latest corrected edition of Beethoven's scores. Also, you get more music with Endellion: The 1799 version of op. 18/1, the H34, the string quintets, some short pieces and fragments.
Why a box set? Because it's cheap and it will be your reference for the rest of your life.
Where to start? Op. 18 (all six), 59/1, 74, and 135 (es muss sein...) should be mighty fine.
Op. 95 is a little brute or a little softie, depending on who's playing, so I cannot really recommend it as a starter. But if you have a need for speed try the Hagen Quartett and get the best Schubert D887 I've heard at the same time.
The Endellion set is availabe at Amazon whereas the Hagen disc is on ArkivMusic or available as mp3@320kbps from Deutsche Grammophon.