What are the benefits of catching a Pokemon I caught before?

The only way to evolve is through candies. you receive candies catching pokemon that you already have (and its evolution branch), hatching eggs or transfering them to the proffesor. so if you catch a lot, you can evolve the ones with highest CP

Also, you win XP to level up your trainer


If you ever want to evolve and train that type of Pokemon, then yes, you should be catching them all.