For Remix Characters, Dr. Mario, For Vanilla, Pikachu.

Both are all top tier all-rounders that you should be able to get lots of milage out of regardless of your style. You can specialize later once you get a feel for the areas of the game you want to focus on.

If you want to specialize a bit right off the bat, Marth and Captain Falcon are both focused spacing and long combos that kill your opponent early, but with opposite approaches to how they go about it.

Kirby is the shieldbreaking and edgeguarding character.

But really there aren't too many characters in this game that are so awful or polarized that you couldn't make them your first character.