The Battle Chateau welcomes you.
New trainers every six minutes. Once you have the Dukes and Duchesses, using the Prize Money O-Power really adds up; catching a Gym Leader with the O-Power active nets you a cool 24,000 at Lv.2. You can nail three or four that are near each other (usually in two rooms) if they are all Baron or Viscount level since the battles go quickly, but if you run into two Marchionesses you might only get two battles. Even so, the financial increase counts! Over 400,000 in one day and that's where I stopped only because I took a breeding break.
Regarding stylishness, go buy Premier Balls one at a time (only place to buy them in all of the games, actually). Every purchase gets you two style points. Go buy some Leaf, Fire, and Water stones; each purchase gets you two style points. Don't buy multiple; that's only one purchase in each shop. Buy one at a time. It takes, without any other points (I'll include the five for meeting Alexa in the Cafe, but nothing else), 125 individual purchases to max out your style. I'm up to 130 Style Points (I tested by trying to access Sushi High Roller, hence how I know), and will likely keep working at it, but want to try other things as well now.