In my experience, there are two paradigms of play, two reasons for playing. Both of them will always be true to some extent, but one is usually more important to an individual than the other.
These players want their characters to come up against and beat increasingly difficult challenges. Mostly, this means fighting monsters, but it can include solving puzzles, persuading NPCs, and whatever else you as a GM can think up. For people with a focus on winning, the plot is mostly a way to get them to the next challenge. Their characters are often (though by no means always) fairly static — their personalities don’t change that much over time. During character creation, their focus is on how to make the most powerful character they can.
These players are interested in collectively telling a good story along with the other players and the GM. Plot and character development are much more important for them. The characters they make will often come with built-in flaws, which the player will want to exploit at the character’s expense. Players interested in storytelling will kind of want their characters to fail from time to time, since this is more compelling narratively. During character creation, their focus is on how to make the most interesting character they can.
It is almost inevitable, however, that play styles are going to clash. Even if every one of your players is interested in only one of these two broad categories (and it's almost certain that they won't be), people will have different play styles in some other sense. One of my players, Hamster, loves the more adventurous elements of our roleplay. When we haven't done anything exciting for a while, she'll say, "Come on, let's get to the plot." But Puppy, another player, loves character interactions. I think he would be okay if the whole roleplay was a high school soap opera. So, as a GM I have to find a good mix between those things.
Basically, to sum it all up: make sure that every time you play, there's something for every player to enjoy.