Pokémon Stadium is a game which in real-life went out in Japan on 1 August 1998 for the Nintendo 64 and which could generously be described as a published demo for a game which was published under that name in North America, Australia and Europe and as Pokémon Stadium 2 in Japan on 30 April 1999 for the same console. This is a take on the latter game as it would have taken place in the alternative universe as described in Pokémon Gold and Silver Versions, within which the demo version would not have existed, and this game would have been released around 25 May 1998 (68 days earlier than in real-life, just like Pokémon Gold and Silver Versions) and for the Nintendo 64DD, which would have made its original late 1997 release date (instead of the December 1999 it was actually released in). As a result, the game would have been able to connect to Randnet, the system's dedicated web service, and thus the game's multiplayer options would have been open to play against others a full three generations early.
In Poké Cup Round 1 Poké Ball, all the trainers' Pokémon are level 50, and in Poké Cup Round 1 Great Ball and Round 2 Poké Ball, all the trainers' Pokémon are level 51. The Twins use paired Pokémon, and will pick one from each pair, while the Juggler in Round 1 exclusively uses Metronome and either Magnitude or Psywave (and in round 2 Present); the Firebreather in Round 1 uses Pokémon who can learn Will-O-Wisp and in Round 2 uses Fire type Pokémon and Pokémon who can learn Heat Wave, the Channeler uses moves which inflict confusion and the Tamer uses moves that have a high critical hit ratio.
As in real-life, Pokémon in Prime Cup are 'maxed out' at level 100. The Teacher uses Baton Pass and assorted stat boosters, while Rocket uses Toxic and Protect and the Black Belt uses Focus Energy. The Gamer uses Zap Cannon and Dynamicpunch in Poké Ball and Ultra Ball, one-hit knockout moves in Great Ball and Master Ball and Lock-On or Mind Reader in Round 2; the Round 1 Scientist uses binding moves in Poké Ball and Ultra Ball and recovery moves in Great Ball and Master Ball and the Round 2 Scientist uses Sunny Day throughout and Fire Spin in Poké Ball and Ultra Ball and weather-dependent recovery moves in Great Ball and Ultra Ball. Pikachu can be taught moves by clearing the Master Ball division of Prime Cup as per similar requirements of real-life, except it can be taught Surf by clearing Round 1 and Fly by clearing Round 2.
The Petit Cup requiring Pokémon between levels 25 and 30 is an artifact from before breeding existed (i.e. the reason it was that high is because that's the lowest it could be so that all Pokémon eligible could be used), so I'm going to head straight down to level 1. And it admits only Pokémon who can evolve, so essentially Little Cup rules. The Student uses Hidden Power, the Sailor uses Steel-type moves and the Super Nerd likes to use Explosion.
The Gym Leader Castle contains all eighteen of the gym leaders in Pokémon Red and Green Versions, six each in Poké Ball, Great Ball and Ultra Ball, followed by the Elite Six in Master Ball. Unlike real-life, the Gym Leader Castle uses level 100 Pokémon, because I consider it implausible that twenty four different trainers just happen to have fifty one different Pokémon lying around so the player can have a choice.