Personally, I'll watch the games out of interest, but when the Phils are not in the playoffs, I don't have much of a preference for who wins the Wild Card game (which I agree is a terrible way to decide anything in baseball). If I do have any preferences, it's more along the lines of rooting against a team that I dislike. If the Mets were in the playoffs, or the Nationals were in the playoffs, I would root against them regardless of who they were playing.

In the Dodgers-Cardinals Wild Card game, I'm not a big fan of either organization, so I'm pretty neutral on the game. My dislike for the Cards is probably not quite as high as my dislike for the Dodgers, but it's a pretty small degree of difference. And the winner has to play the Giants, who I'm not a great fan of either, so I really have no preference in that part of the bracket.
I'm not a big fan of the Brewers, but my dislike for the Braves is much greater, so I will root for the Brewers in that series.
The AL matchups are more intriguing to me, perhaps in part because the Phils are part of the NL, so I don't have a lot of rivalry or other type of feelings against those teams. The Red Sox-Yankees Wild Card is crazy. Those two teams, and their fan bases, despise each other, and it all comes down to one game. The winner of that game plays the Rays. I respect the Rays, as they've been able over the years to put together teams that could compete with and even beat the money that the Red Sox and the Yankees have. As such, I'll probably root for the Rays in that series. The other matchup is the White Sox-Astros. I'll probably root for the Sox, in part because they haven't had a lot of success over the years.
MLB playoff games are always fascinating, especially with the way every move, every pitch, etc. can be discussed, debated, argued about for decades after the fact.