I think my favorite weapon to use is the tri-forked Lizal boomerang. It's fast and furious, and has a pretty decent damage rating and decent durability. However, the royal broadswords and lynel swords with really high damage are better, as they are almost as fast, but do so much more damage with each hit.
Now, getting into favorites of each "class" ... I will list below, but they all go to Savage Lynel items:
- Favorite/Best one-hander: Savage Lynel Sword with 90+ damage rating
- Favorite/Best two-hander: Savage Lynel Crusher with 100+ damage rating
- Favorite/Best spear: Savage Lynel Spear with high damage rating
- Favorite/Best Bow (for normal use - see below about ancient bow): Savage Lynel Bow with either 3 or 5 shot burst (if you look at the damage for each, they are CLOSE to the same. I'm not in front of my console, so I don't have the exact numbers ... but the damage per arrow on the 3-shot bows is higher than that of the 5 ... so the 5 IS stronger overall, but ONLY if you can hit your target with all 5 arrows at the same time - meaning, you have to be close to them. The 3-shot bow trumps the 5 with longer range shots, as you have a better chance of hitting 3 arrows, each with higher damage than that of the 5-shot version)
- Favorite/Best Shield (for normal use - see below about ancient shield): Honestly, that easily goes to the Hylian shield (or Goddess, or whatever it is) ... the one with 800 durability. However, given the ability to do the perfect parry, a pot-lid will do just as well, since that eliminates any damage to the shield at all.
Don't get me wrong ... ancient weapons (Axes and Swords) are great on guardians ... and elemental weapons have their place. There are many other weapons I like besides my "favorites" ... but if we're all being fair here, the numbers don't lie. The durability and damage ratings on those high-end Savage Lynel weapons cannot be beaten.
ANCIENT BOW AND SHIELD: both the ancient bow and ancient shield are quite formidable, if going against guardians. The fact that the ancient shield requires no parry to reflect the laser from a guardian makes it an amazing shield to have. Likewise, the "range" of the ancient bow makes it a must-have for accurate long range shots ... which comes in VERY handy on both guardians AND for when you're farming dragon parts. It's pretty satisfying to be in slow-mo drawing the bow on the dragons and knowing you're going them right where you want, and get the "part" you want/need.