Iphone 4s version 6

I have an Iphone 4s version 6.0 (10A403) and would like to update to a newer version maybe 6.1.1 or 6.1.2 and then jailbrake my phone with evasion, but i'm not entirely sure on how to do this.
Sure i stay with this version 6.0 (10A403) or can i update to newer versions and how do i do it without connecting to Itunes since the newer version would not allowed me to jaibrake.

Can i use evasi0n with 6.0?
Please any help or links wwould be very much appreciated.