It's really simple: if you want to win the NLCS, win game 1. If you want to win the World Series, finish the LCS first.
Since the beginnning of the three-tier playoffs in 1995, the team that won game 1 of the NLCS is 9-2 in the series. What does that mean? Maybe not much considering that both the '03 Marlins and '96 Braves won game 1, lost 2-4 and won the NLCS. The ALCS game 1 winner is as often the loser of the series (5-6).
As for World Series winners -- every World Series champion since 1995, except the 2000 Yankees, is the team that first finished off its opponent in the LCS. I wouldn't suggest this is anything more than a trend, after all the '96 Yanks polished off the Orioles, had to wait to learn their opponent, and promptly got waxed in games 1 and 2 of the World Series. Then again, in each of the five years that the NL and AL champs took the same number of games to win the LCS, the team that clinched first won the Series ('97 = Marlins, '01 = D'Backs, '02 = Angels, '03 = Marlins, '04 = Blosax).