I've had plenty of characters who influenced events without a lot of effort. The trick is MOST PLAYERS want to play a badass. This similar to real life in that people want to be "heroes" or "remembered". If you only work towards your benefit, you will find less enemies and more friends. Only befriend those who will aid you and you will reap the benefits. Never work for the weakest side. That way only leads to failure.

Make a character who is focused on self interest, even if they aren't aware that they are. Maybe play a mercenary who only works for the people who pay him most. Maybe, they want to do the "right thing" but aren't quite sure what that is. Maybe they're a hypocrite. Being a warrior means they bring blood, but wanting to do the right thing means more killing. Maybe they can't accept they're a killer.

The trick to being interesting is finding your own style. People who act outside of boundaries are most remembered. Play someone "mundane" but with a unique perspective and motives, maybe.