it is important to consider the quote that Sakurai has about Pokemon. Essentially its not only about the games, its about which Pokemon are consistently used, are popular, and hold relevance in the series. By the series, I mean the games, movies and animes. The exception is Jigglypuff, but being a Smash 64 veteran holds a lot of power.
Pikachu: available in all the games, in the anime is Ash's favorite. Hes the face of the series, so having him makes sense. Very recognizable even to people who know nothing about Pokemon. No brainer.
Jigglypuff: a little bit of an exception, but as I said earlier, being a 64 veteran is a pretty important. When 64 was made, Jiggs was one of the most recognizable and famous Pokemon (especially in Japan.) The series was very young at the time, and maybe Sakurai at the time thought it was a good idea (similar to Kirby? You know, his own series that he created? Easy to create? I dont know im just spitballing) It could have easily been Meowth in this position, but thats how the process of selecting characters goes. If you miss the boat once, that could have been the only opportunity.
Pichu: we know about the clones created in melee which is why he was selected, being similar to Pikachu. He was important to the anime at the time, and his popularity has dried out now. He was featured in the games as a pre evolution to Pikachu, the most important pokemon to the series.
Mewtwo: legendary in a lot of games, featured heavily im the movies. Very famous and recognizable.
Lucario: essentially the next Mewtwo. Featured heavily in the movies, important in the games since he was created. Very famous and recognizable.
Pokemon Trainer (Charizard, Squirtle, Ivysaur): its the trainer you play as, plays heavily off of Ash and Red. These were the starters in the original game, and are atill the most recognizable and famous ones to this day. Charizard is very popular and recognizable, so he was an obvious pick along his evolution line. Squirtle had a major role in the anime (squirtle squad, 007, etc.) So he made sense for that choice along his evolution line. And then Ivysaur was the mid point between the two. Basically, these characters are important across the board.
We can't deny the importance of the anime, but at the same time the games are probably what holds more weight when choosing characters. The anime definitely has some importance in Smash. The characters that are chosen are Important, popular, relevant, famous and recognizable across all mediums of entertainment.