Your character can have one of two basic motivations.

(1) Motivation is to finish a specific quest. This is a character with a strong will, like the paladin you mentioned, who has obvious loyalties. It's clear this person is going on a quest and the party can join them. They shouldn't just tag along with the disinterested party imploring them to join the quest. The party can choose whether to stick with him, or part ways, or maybe meet back up with him later.

(2) Motivation is to stick with the party. This character shouldn't have such a strong will. They can have a strong personality, but they shouldn't be making decisions for the group at any point, or you are overstepping your role as a DM. They should have something they want to accomplish but it shouldn't be as urgent as #1. Like maybe they want to find their father's murderer, which will be a plot hook in the future. Maybe they just are a loner and want some protection. Maybe they admire the party and want to learn from them. Maybe they just enjoy getting into fights.

(1) can turn into (2) if you are thoughtful about why. Maybe the paladin is super dedicated but something happens to shake his faith and then he joins the party.