To me RP is characterization. That is taking some basic characteristics and letting your character's personality develop from there. For me situations may occur that can change your character but the basics characteristics should remind unless there a a traumatic event that effects that.
For example:
If you have a nice character and they travel through the towns frequently and do not greet others on a regular basis they are not so nice
or, if you have a bad character and they do go through towns greeting everyone they are not so bad. Unless they are secretly bad and that is the ploy they hide behind. I have met a few like that.
Because of those basic characteristics, it may or may not be hard to find a place for your character in one of the many of the on-going RP Saga's or shorter story based RP's. That's the great thing about Characterization is that it creates a struggle for your character. Should they cross that line or not? What happens if they do? Does your character have the experience to avoid the situation somehow?
This is how I approach these types of RP's. Many do not fit the characteristics of my character. There may be a small part in there that I can play and that is what I look for. Supporting cast would be a good term for it. That can be just as interesting as being the main player of the RP. One does have to remember that many Saga's and Story based RP's operate with a designed direction. So you have to adjust slightly to that if it exists.
Jaycol for instance is not great with weapons or anything else. He will never win a battle for you and because he upholds the CoD creed of peace he most likely won't join you either. He does enjoy a watching a good fight however, so is more likely to show up on a hillside with a supply of beer and make bets on which side wins. He also is not stupid so he isn't going to find himself as a victim 9 out of 10 times. His friendly nature may get him in trouble , but his experience in the outlands allows him to sense and avoid it most of the time. In short he never goes looking for it.
This is the style and approach I use. It may not fit anyone else's style or preference of play due to their choice, experience, available play time, or what they find entertaining. It is after all a game. The thing I like about PS is that it is open ended. Meaning that I control the direction of game play for my character. So if he falls off a cliff tomorrow, bangs his head, and forgets who he is and has to start over again and goes in a different direction that is okay too.