I know there are a lot of variance here, but are there any personalities/dynamics that a superhero team needs in order to work? Any advice will be greatly appreciated.
A superhero team is first of all a team. You might therefore find the question How to write a story about a team? useful.
With that in hand, you must also determine whether your team are all superheroes, or there's just the one superhero and the rest are regular people.
If your team is a team of superheroes, their superpowers, like their traits, should complement each other. If one superhero is significantly more powerful than the others, his power makes the others superfluous, unnecessary. Each superpower, each team member, should be necessary for the team to achieve its goal. So you must take care to balance the powers, never making one character overpowered or underpowered compared to the rest.
If your team is the "support staff" for the one superhero, you must answer for yourself why each member of the team is necessary, why the superhero needs them. What do they provide that he doesn't have? Without this team, the superhero cannot succeed. So there must be an answer why he cannot succeed without this group of seemingly regular, weak people.
As in any team, there need to be opposing traits - for someone shy and secretive, add someone outgoing. For someone idealistic, add someone pragmatic. Etc. Bouncing against their opposing trait, each shines, each is seen better. And each in turn has its place, necessary for the team's success.
But as for particulars, any traits, any personalities can make a good story.
There are a number of different directions that one could take a superhero team, each with their own unique personalities. That said, a good starting point, one which many superhero teams leverage, are an "idealist" and a "realist".
As people with extraordinary abilities, we should be held to an extraordinary standard. We have gifts, and it's our duty to use those gifts to do the right thing, regardless of the situation. We can't afford to make compromises, because we're the heroes that the rest of the world looks up to. If we start cutting corners with our morals, what kind of a message does that send?
The world is a complicated place. Ideas like "good" and "evil", "right" and "wrong"? They're luxuries that we can't afford. Our mission begins and ends with helping those who can't help themselves, and stopping those who would do harm to others. That's it. Trying to play by the rules and fighting fair are just going to get people killed.
You can modify these to suit your story, but you get the general idea. Having two voices like this on your team naturally bounce off of each other, and gives you an easy way to explore some of the more complicated nature of a team of superheroes. Common examples of characters that roughly fit into a model such as this include Batman and Superman of the Justice League, and Captain America and Iron Man in the Avengers (at least as far as the MCU is concerned. I'm not familiar enough with the comics to know whether they have a similar dynamic there)