My favorite bow would be the Royal bow, for sure. I love the design and it's strong. Next would be the Steel Lizal Bow, also has a cool design and is strong. 3rd would be the Savage Lynel Bow, it's useful to deal lots of damage quickly if you're in a pinch.
The Royal Broadsword, I love it's design. The Frostblade and Frostpear would be next, their designs are awesome and I love ice weapons. Ice is the most useful of the 3 elements imo.