Part of it may depends on which deity you are a Paladin of. Im not familiar with the Pathfinder Pantheon.
A good example of a Lawful Good character would be Captain America. He always stands up for the underdog and works for fairness.
If you have it in you, play up your Charisma. Give speeches of inspiration. Don’t be afraid to take charge. Be the first to speak upwhen the party is questioned, or if you see something wrong happening. Do your best to work within the social structures of whatever government may be local, but should they prove to be corrupt, bring forth the fury.
Another aspect to consider if your characters love/sex life. If this is a topic that may make some players uncomfortable, adjust it as you see fit. But, is your character a virgin? What are his views on sex? Does he get shy and flustered around women? Does he have a family that he fights to protect? Does this cause to to become very protective of children?
So many players create their characters that exist in a vacuum. No family. No parents. Because god forbid those things be used against the player. Thats boring.
Of course you could talk to your GM about being more a “Holy Warrior” and not a Paladin, per se, if you wanted to follow a more violent Deity. I always felt the alignment restriction on Paladins was kinda stupid. And before 3rd Edition, only Humans could become them as well. With a required Charisma of 17+. Meh. Thats another rant.
Read the DC graphic novel Kingdom Come. Check out Superman in that story. He is the epitome of Lawful Good. Even if you are not a fan of Supes, the story is excellent.
I hope this helps. Good luck.