Question: What kind of personality should my protagonist have?
Some writers would say this question puts the cart before the horse, that it's better to start with a character and build the story around him/her.
However, let's say you are the type of writer who begins with a story idea rather than a character. Generally, that means a world where there is some sort of problem, threat, or imbalance that needs to be resolved.
The choice of main character can be seen as a choice of values. You might ask yourself what it will take to solve the story problem. What type of values, principles, or approaches are required?
For instance, will it take courage? An outsider's perspective? Innocence? Caring? Wisdom? Commitment? An openness to ideas? A unique talent or skill? A unique background? The right attitude?
If you intend your protagonist to succeed in achieving the goal, then one approach is to create someone who has the unique quality needed to succeed -- a quality none of the other characters possesses.
If your protagonist is also the main character (a common choice), then you probably want to give him/her an inner conflict.
For instance, the character may have what he needs to succeed, but something may be holding him back. He may be wedded to a particular approach that may not work in this situation. In the course of the story, He will then be pressured to change, to switch to a different approach (which also may or may not be the right one).
At the character's personal crisis, they will be forced to decide whether or not to change, and that choice will determine whether they are able to achieve the story goal.
Choosing these two traits will give you a character who will
fit nicely into your story, a character who is a suitable protagonist who must grow as a person in order to succeed.
After that, you have a lot of scope to develop other aspects of the character's personality in any way that makes sense to you. A few surprising or even contradictory traits can make for a more interesting character (since real people are often a little inconsistent).
You can think about personality in terms of...
Background: how the character's environment and experiences in the past may affect their personality.
Physical traits. Sometimes a person's body affects how other people treat them, which in turn affects how they see themselves.
External traits: Think of some adjectives another person might use to describe the character (e.g. stuffy, light-hearted, generous, snobbish, shy, vivacious, etc.)
Then there are internal traits, such as...
Purposes: What does the character want (both immediately and long-term)?
Methods: What is the character comfortable/not comfortable doing? How does the character typically deal with challenges?
Motivations: What drives the character emotionally? What feelings influence his behaviour? Does he have a chip on his shoulder or a hole in his heart?
Evaluations: What does the character think about himself or others? What beliefs, principles, etc. affect his behaviour?
It can also be useful to consider whether you want to write a story about a likely or an unlikely hero. Some heroes are in their element when tackling the story goal, while others seem like fish out of water.
Two final considerations.
1. Create a character who you want to write about -- someone who you can emotionally connect with as you write.
2. Create a character your ideal reader can also connect with emotionally. This is especially true if you are writing for a particular age group or gender.