There are two cardinally different ways you can treat your characters in a series.
In some series, the characters remain the same, facing the "challenge of the week". They do not undergo any significant change themselves. A famous example of such structure is Star Trek, the Original Series. Kirk, Spock and McCoy do not undergo any character development in the three years of the series' run. In fact they remain fixtures to such an extent that each got their TV Trope: The Kirk, The Spock, The McCoy. In each episode the setting is different, but the audience can expect the same interactions from the characters. A significant part of the series' attraction lies in those interactions.
For a series to pull this off, the characters must from the start have the traits that would enable interesting interactions. They need to be on opposing ends of some spectrum, so that in each other's company they shine the brighter. And at the same time, each needs to be engaging, have enough depth that the interactions don't get repetitive.
A literary example of the same style of storytelling is Sherlock Holmes: from story to story, Holmes doesn't change. Neither does Watson. Each time, we are curious to see how Holmes will solve the mystery. The innovation of the mystery, combined with the familiar character of Holmes, can carry the series indefinitely.
In other series, significantly more focus is given to character development. Personalities evolve. The character at the end of a season isn't the same as they were at the start of the season - they learn, they change, they are affected by the story. A greater part of the screen-time is given to character development, as opposed to "the challenge of the week", episodes have an effect on the characters, including repercussions. Dollhouse comes to mind as an example. Or Buffy.
For such a premise, you need to give your characters, at least the main ones, room to change and evolve. They need to be sufficiently complex to support an internal conflict, preferably something that can be explored again and again - there needs to be some sort of tension inside them. For example, Buffy has the ongoing issue of being the Slayer vs. wanting to have a normal life. Various aspects of this are explored. (There are also other issues, for the same character, and for others - one character cannot carry a series on their shoulders.) So when you plan the character, you define an inner tension for them right from the start. Maybe, as the story progresses, you will find that this isn't enough, so you resolve it, and add another issue instead - like Willow's nerdy identity got "outgrown", and she got the magic issues instead. But you start with something. You don't start with characters who are already pretty much where they want to be.
In either case, you also need to consider how the characters would interact with each other. If you're planning a team, you need complementary traits. Look here for more information. If you want conflicts and opposing factions, consider what conflicts can be had, and plan for them, put in place characters who would have reason not to like each other. Put in the tension, then you can play with it however best suits your stories.