National League Teams:
Arizona Diamondbacks
Atlanta Braves
Chicago Cubs
Cincinnati Reds
Colorado Rockies
Florida Marlins
Houston Astros
Los Angeles Dodgers
Milwaukee Brewers
New York Mets
Philadelphia Phillies
Pittsburgh Pirates
San Diego Padres
San Francisco Giants
St. Louis Cardinals
Washington Nationals
As long as you pick one of these teams and beat every event in the Rookie Challenge (the last of these is the World Series), you should get this one.
As for the best team to use, I'd recommend the St Louis Cardinals. They have a pitcher with high stats, and their hitters (Albert Pujols in particular) are solid.
The QUICKEST way to get through this mode is to bunt your way through the games. Just score one run at one point in the game (or more, if the scenario calls for it), and just hold X everytime you're at bat. You'll almost always get thrown out, and burn through the innings.
Also, don't worry so much about bumping your rookie stats up. Near the end (70% complete, approximately), you get to play Home Run Pinball with your rookie. If you follow my strategy for the 1,000,000 points, you can bump up the majority, if not all, of your rookies stats.
Good luck. Rookie Challenge is not tough, but it's surprisingly boring on the second go-round.