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.

This site will help you in all you need.

evasi0n iOS 6.x Jailbreak - official website of the evad3rs

But personally, if you needing instructions about iOS and JailBreaking a device, just be careful once you have, in Cydia as to what tweaks you put on your phone.
Every iOS Apple bring out, there adding some of the best things that the JB community have, hence i dont JB anymore as i have no need.

Be caeful when updating your iPhone, as iOS 6.1.3 is now available for download, and there isnt a JB for 6.1.3 yet, so if you update to 6.1.3 you wont be able to JB your phone. And if you want to goto 6.1.2 you need the correct .ispw and you can get it from here.

Good luck

I'd advise to upgrade to iOS 6.1.3. Been using on my 3GS since it was released. Not a speck of trouble with it.