In the game, there are six characters that can join your team. Sadly, the main character can be accompanied by no more than three party members. Each character has their own, separate story, unique interactions and even quests that can be completed.
The game is designed to provide fun by using different play styles, so that each playthrough offers new things to discover etc. The same goes for companions - when you complete the game once you won't be able to discover all the character combinations, you won't read all of the interesting conversations and learn about their stories. The final choice is done in Sagus Cliffs - when you leave that location, you can't go back and recruit other characters.
Your stay in Sagus Cliffs (the first major city you'll encounter during the game) will enable you to visit the available party members during their mundane activities. Unfortunately, the main storyline involves choosing a fixed group that will accompany you to the next major area of the game. If you want to be able to make changes, make sure to find the Bronze Sphere before leaving Sagus Cliffs. The Sphere is a unique artifact that can be found in Buried Crossroads (the part of Sanctuary of the Changing God) (M11.8). More details on how to acquire this artifact can be found in the captions for Map 11 (M11) and in How to change the party's composition beyond Sagus Cliffs?
When it comes to the choice of your companions, your character's main class certainly plays a big role. If you, for example, play as a Nano and want to specialize in spells then Callistege won't be that useful and a better solution is to recruit, e.g.: Tybir/Erritis. Aligern is also a good choice and can be used in any team because he can heal others.
Rhin is a hard nut to crack - she is a girl that, for almost the entire game, is more of a hindrance then help in fights. But with time, you can discover her true self and strengthen her. However, she certainly is not an ideal teammate - at least when it comes to combat.
Matkina, on the other hand, is a good choice for any party - she is a skilled assassin that is really useful in fights. She should be combined with Erritis, for interesting interactions, creating a very powerful team to fight in the first line. Aligern/Callistege is a perfect support for them. With a party like that, regardless of your character's class, you can easily deal with any enemy.
But remember that the choice is yours and if you want to focus on the story and learn about the world then choose the characters that are the most interesting to you.