Fighters are good damage-dealers and has the 2nd highest defense (the 1st is Knight). Fighters pair often with Mages and Bow Rogues for massive damage. There are two types of Fighters. Sword and Axe Fighters. Fighters can cure status ailments on them self and prevent some status. Fighters are also the only ones that have the skills Meat Eater (ミートイーター), Genocide Task (ジェノサイドタスク) and Double Attack (ダブルアタック).
Sword Fighters are good damage dealers and have lots of useful skills in battle. Notable skills are Attack Kill (アタックキル) that does ATK down to an enemy and Elemental Follower (エレメントフォロア) that "follows" a Mage spell and attacks the target with the same element. Fighters is the only class that can use physical full-party attacks with no requirement (Knights must have a dead party member to do full party attack and Iai Samurai must use up an EX) so they're pretty good at clearing mobs. Swords deals Slashing damage.
Axe Fighters deals more damage than Swords, but they are much slower than Sword Fighters (and other classes). Notable skills are Balance Kill (バランスキル) which does resistance down to a enemy, Purge (パージ) that does massive damage and instant death under a certain LIFE and Arrow Follower (アローフォロア) that "follows" a Bow Rogue's attack for massive damage. Axe Fighters EX skill, Tidal Wave (タイダルウェイブ) has a chance of inflict skill-seal, which is very useful. Also, axes deals Blunt damage.
You can always pick up Double Attack, though, if you want to use Double Attack you have to spend 5 SP at the opposite mastery skill, which is not necessary. If you don't have a Healer or a Princess, you might want to pick up Berserk (ベルセルク) and Endorphin (エンドルフィン). There are 2 kinds of common Fighters:
Sword Fighters main attack is Attack Kill for bosses/dragons. Pick Element Follower if you have a Mage or Fang Blade (ファングブレード) if you don't. Element Follow needs Defense Switch (デフェンシブスイッチ) and Fang Blade needs Offensive Switch (オフェンシブスイッチ)</span> so be sure to pick one of them. Max Sword Mastery (ソードマスタリー) and pick up Rush Edge (ラッシュエッジ) (グランドバスター) for random encounters. If you want, you can level up Keen Edge (キーンエッジ).
Axe Fighters main attack is Purge (or Power Crash, though Purge is more recommended). Pick up Arrow Follower if you have a Bow Rogue, Balance Kill if your party relies on status ailments or Defend Kill (ディフェンドキル) if you don't rely on any of those. Arrow Follower requires Offensive Switch, so be sure to pick it up. Max Axe Mastery (アクスマスタリー) and pick up the EX skill Tidal Wave. You can take Shield Axe or Stun Bash if you want. But, Shield Axe requires Defense Switch so you don't need to pick it if you're lacking SP, though this will get your survival sky high at max. Stun Bash has a high chance of Stun (makes your enemy go last) but Axe Fighters are pretty slow, so the Stun effect isn't going to work.