Nintendo Cup 99 is not quite the same as Poke Cup from the English or other versions. In this cup, the level requirement range is 1 ~ 50, with no combined levels restriction whatsoever. Generally recommended to just bring level 50 pokemons.
And also, most of the Gen 1 bad boys are banned from this cup(ex: Snorlaxes, Tauroses, Alakazams, Starmies, etc.) That said, there are still some top tiers for this cup.

Reason for my pokemon choices:

Raichu - Show off his surfing skills. Other than that, I like the coverage with surf, and he's a decent pick in this cup.

Charizard - Best fire Pokemon in Gen 1 was not banned from this cup (cus fire typing is garbo). He outspeeds most of the Pokemons in this cup, and has good attack choices.

Blastoice - He's selected only because he can fire hydropump off his biologically integrated cannon

Mr. Mime - I chose him because I didn't want to use Kadabra

Haunter - His typing makes a lot of matchups easier for this cup (especially against Persian). His special stats are so great that even without STAB he can deal significant damage. He also takes little damage from special attacks that come from Pokemons with low special

Porygon - A toy for testing