This favorite Pokémon chooser presents you with 2 Pokémon to choose from. Click (or hit the corresponding arrow key) to select the Pokémon you prefer.
You don't have to base your decisions based on who's your favorite, though: you can base it on whatever you want! Cutest Pokémon, most useful Pokémon, the list goes on.
To choose a set of Pokémon, select from the dropdown list labelled "Pokémon" with the default value "All". From this list, there are 3 groups: Generations, Categories, and Megas. In the Generations group, the options are to choose all generations (the default) or the individual generations. Choosing all will allow you to use all Pokémon and choosing a specific generation will choose the Pokémon introduced in that generation. In the Categories group, there is a group of miscellaneous collections of Pokémon. In the Megas group, you can choose to play with every Pokémon including the mega evolutions, the Generation VI Pokémon including megas, and only the megas.
Checking off the "Only Pokémon from Selection" will only include Pokémon from the selected set. Otherwise, it includes all of the Pokémon from the preceding categories in the group. Some sets are automatically set to a certain configuration for this option and cannot be changed.