Hey Apis, it sounds like you weren't sure if you were going to like the game, sped run it, then realized you might actually be starting to like it. You're missing some key basics that are explained very early in game in the tips screens.
Stats aren't a requirement for any story to occur, and money is best earned first through the farm, then the bar, which you should have leveled a bit by now.
But I'm confused by your timeline of events. You're saying that Lin's story is ready to continue with the competition, but are also getting told to buy Sylvia, who you meet during the competition? You can only buy her after.