Which custom or official kernel should I use on SGS2?
Upgrade your phone to latest JellyBean stock ROM and flash SpeedMod kernel from Odin. Right now is one of the most stable combinations for the Galaxy S II.

If you want more performance you can always install Siyah kernel and tweak it for your needs.

Also remember to do a full Nandroid backup before flashing anything and wipe /system, /data and /cache before installing JB from Odin.