There is no best gun to carry, just different setups depending on your situation and what your wanna do like most have mentioned.
Hunting: bolt action/Springfield rifle, varmint rifle, double sawed off shotguns.
Free roam missions: Springfield rifle, double sawed off, bow with dynamite arrows loaded
Showdown (generally): double Scofield revolvers, either Springfield or bolt action, repeating shotgun.
Varies a little depending on my card set up too.