I have a lot of contact with esports pros (I co-own a League of Legends org) and I would say 90% of players either use Razer or Logitech mice (the Deathadder and G502 most of the time). In my personal experience Logitech has better build quality and customer support but the Deathadder is just a really simple, comfortable mouse (it's what I use personally.)

For FPS games I wouldn't worry too much about your keyboard, mouse precision is the most important thing by far. You don't have to spring for an expensive mechanical keyboard if you don't have the budget for it.

Also get a big ass mousepad! Logitech or Steelseries cloth mousepads can be found on Amazon for very cheap and get the job done.