Scissors because it's the one that hasn't been thrown in this thread yet.
Related: I didn't know that, in the Japanese version of Alex Kidd and the Enchanted Castle on the Sega Mega Drive, your opponents in "Jan-Ken-Pon" strip when they lose. In the western version on the Sega Genesis, they just have weights drop on them which grow cartoon eyes and feet.
Scissors. You might not be able to cut through a rock like paper, but you can use it to sharpen the scissors blades, wearing down the rock in the process.
Sometimes I forget what I'm playing while we're doing the thing where you bounce your hands before you make your selection and I usually end up accidentally picking rock and I usually win because scissors are the most interesting one of the three and people usually pick that, so it's a good strategy to be airheaded
Rock, it is the safest choice by far.
The average unsofisticated RPS player will almost always start out with either Rock or Scissors, after all the battle cry goes "Rock! Paper! Scissors", confusing the inexperienced into reacting with the first thing they hear or the last thought that entered their feable minds, opening them up for attack.
Rock protects you from the first and beats the second.
I'm a Scissors main. It's a versatile moveset with good stab and slash dps. It's also able to be used in close and ranged combat quite easily. It's tool useage also heavily outways the other two characters, putting it comfortably into SS tier.