Not every Pokémon in Pokémon Go can be Shiny, and even those which can can still be pretty difficult to track down. Outside of an event, your best chance at finding Shiny Pokémon is to click on every single Pokémon you encounter whose species have the potential to be Shiny. Here's which Pokémon you should be Shiny checking.
If you like to keep some distance between yourself and the monsters you hunt, then you should definitely consider the bow. It's a mid-range weapon that can provide buffs for friends or force status conditions on prey.