If you're doing katana go with the Katana Combat Hitcount Up (L) and Combo Var. PATK PP Save (R). There is an R Ring in a future update that'll make it possible for us to have 100% Crit Rating so we'll always be able to deal max damage, but it might be a while before we see that one. You might want to consider, as L Ring picks, Leaping Dodge which gives i-frames, Atomizer Fanatic which also gives i-frames (also know that the Star and Cosmo Atomizer gives healing), and Katana Focus Guard Release which gives you on demand Gear Release (you have to hold weapon action for 3 seconds though).
As for bow there is Bow Homing which makes charged normal attacks homing as well as PP Conversion which gives the Force skill of the same name (gain more natural PP recover) and Hunter Physique which gives the Hunter skill of the same name (gives damage reduction and knock back resistance).
Oh and there is a Mate Maniac ring if you just want to speed up Mate use animation.
(Note: My information is based on guides.)