Upgrade the bronze bell to the recorder lines. There isn't a "best" HH, because it depends mainly on what you are fighting, but the recorder line of HH gives you all you will ever need to fight any of the elder dragons. Gives you dragon-wind breaker to hunt down Kushala Daora and not get pushed by Lao Shan lungs' foot breeze, Clairevoyance, to always know where the Chameleos is, dragon element damage to be able to break lunastra and teostra's crowns (horns), and if you couple that with armor that negates heat damage, you don't even have to focus on breaking those parts right away, and can just go straight into doing damage. Overall, it is the best for vs Elders.
For all the other monsters, since the Triangle + Circle into a dodge & repeat combo is so quick and delivers many hits over time, just pick a weapon with a good amount of raw, and a decent amount of elemental, and you will be knocking down foes with ease. good rule to follow: Divide the elemental by 2 and add it to the raw damage, if this number is higher than the raw damage alone of a higher raw weapon vs a monster that is weak vs that element... take that elemental weapon.
One thing you will notice, is that every element seems to have the tones that give you advantages when fighting monsters that live in that particular terrain. So the "Electric Guitar" that has fire element damage, also plays music that gives you unlimited stamina, and cold protection, and stun protection... great when fighting monsters weak to fire within an ice enviroment, like Ukanlos, or Blangonga.
Horn durantion up is very easy to gem into any armor, so focus on getting other skills that you might want more. Evasion up, for example, from the insect armor, would be great. You can then Gem it to have Sharpness+1 AND horn duration up... giving you a killer combination for a hunting horn user.