Sanosuke learns 1 new technique from Monk Anji during the Shishio Arc. Other than that, he doesn't grow to be all that powerful.
As for the anime, it follows the manga up until the end of the Shishio Arc. (Which is around Episode 61-63. There is a total of 95 or 99 episodes to the anime though.)
(Edit: Also, when you reach the end of the Shishio Arc in the manga, I would recommend watching the OVA Trust and Betrayal before continuing forward.)
Edited by Ren-san, 09 July 2013 - 09:50 PM.