Basically what I am doing is offering up an additional class ability, one that the player gets to pick for their character. It adds some new special abilities and a bit of customization to a character. The player picks one Fighter Style during character creation, and is stuck with it for the duration of their character. These styles also add a bit of flavor to your character, giving you (as the player) some story and background hooks into the character. This can end up helping with the role-playing of your character as much as it can help with the gaming of it.
I know that this is going out of the boundaries of old school play, for some, but my approach is that I am looking for a simpler approach to gaming, which games like Swords & Wizardry and Labyrinth Lord supply for me, which I can then customize to fit the needs that the group and I have for play. So far that has meant bolting on this rudimentary advantage system onto the character classes. This approach has worked well with our party cleric, without making it out of proportionally more powerful when compared to the other characters in the group. It may not work for everyone, but it works for us.
Furious Style
The fighter's early years were spent among the savage outlanders who taught them to fight ferociously, and with all of their body and spirit. The fighter's first attack against an opponent receives a +2 to hit and damage. They also receive a +1 to saving throws against cold.
Florentine Style
The fighter has been trained in the art of fighting with two matched weapons. When fighting like this, the fighter receives an additional +1 to their to hit roll and a -1 [+1] to their armor class. The Florentine fighter can only receive these bonuses when they are fighting with two one-handed weapons in a matched pair (two short swords, hand axes, etc.). When an attack roll is a natural 20, the fighter does double damage (simulating a hit with both weapons at the same time).
Acrobatic Style
The fighter's style of fighting is high dynamic and acrobatic, always keeping in motion during a fight. The character receives a +2 to saving throws that require dodging or movement, and a -1 [+1] to their armor class. When not fighting, the character tends to be fidgety and distracted.
Hard Style
Sometime the best fighter is the one left standing at the end of a fight, and your fighter has put a good deal of training and effort into toughening themselves up so that they will be the last one standing. Your fighter receives a bonus of +2 to their hit dice each level, and they get a +1 to their saving throws versus death and poison.
Hand to Hand Style
Your fighter's training taught them that their best weapon is the one that can never be taken away from them, broken or lost: their body. They can use weapons, but their hands and feet are deadly weapons as well, and the character receives a +1 to hit and damage when using them. At 5th level, the fighter's hands and feet are considered to be magical, for the purpose of hitting creatures that can only be hit by magical weapons.
Favored Weapon Style
The fighter has spent extra time and dedication in training with a specific type of weapon. When using a weapon of that type, they receive a +2 to hit and a +1 to damage. You pick the weapon that your fighter specializes in when you create it.
Monster Style
Knowledge can help win a fight. Your fighter has studied the ecology, strengths, weaknesses and tactic of a specific type of creature. When fighting a creature of that type, your fighter receives a +2 to their hit and damage rolls. You have to name the creature type when your create the character (common choices would be zombies, vampires, lizardmen, troglodytes or lycanthropes), and it cannot be changed.