Fighting Styles and Who They're For

A few classes in 5e D&D (fighter, paladin, ranger) have access to Fighting Styles--a small mechanical choice you make about the way your warrior fights. However, it isn't clear what the various options on offer are really good for or what they have synergy with, particularly if you allow feats in your game. In my experience, here's what you need to know to make an informed choice when picking a Fighting Style:

• Archery: Archery is really the only good fighting style if you want to specialize in ranged combat, and it's all about accuracy. Archery gives you a +2 bonus to hit with ranged weapons, which negates the +2 bonus to Armor Class that foes in cover get. That +2 to ranged weapon attacks is already pretty powerful in a game where attack bonus are fairly limited, but taking it and the Sharpshooter feat is one of the most powerful combinations in the game. Although Sharpshooter shots give you a -5 penalty to hit (comparable to having disadvantage on the roll) in return for a massive +10 damage, that +2 to hit from Archery really helps offset the penalty. Characters with the Great Weapon Master feat feel that -5 penalty to hit more deeply because their Fighting Style doesn't get a +2 to compensate, and Archery warriors get to pull this off at range.
• Defense: Defense gives you a +1 bonus to your Armor Class when you're wearing armor, which frankly is a really tepid bonus. However, Champion fighters get to select a second Fighting Style at 10th level; by 10th level you've probably already got your fighting routine down, so you might not get much benefit from picking any of the other Fighting Styles on offer. At that point a +1 to your Armor Class starts to look a bit more appealing since every bit helps when it comes to keeping swords and claws away from your hit points.
• Dueling: The +2 bonus to damage when wielding a one-handed melee weapon is a bit of a red herring; this is a Fighting Style you take when you plan on prioritizing your armor class over your damage. With this Fighting Style you should get the heaviest armor you can or figure out the best combination of Dex bonus and armor for your character; you should also wield a shield for maximizing your chances of not getting hit in combat. The Shield Master feat is a solid choice with this Fighting Style to bolster your defenses even more.
• Great Weapon Fighting: This is the choice you make when damage is more important to you than special effects or defense. Combine this with the Great Weapon Master feat and you have a potentially game-shifting (some say breaking) ability to dish out damage; like Archery, you can take a -5 penalty to hit in return for +10 damage. Note you can get that +10 to damage on all the attacks you make with Extra Attack, so a high level fighter potentially gets +40 damage per round, and +80 damage on rounds where you use Action Surge. And that's before figuring in weapon damage, Strength bonus, Expertise dice, magic, etc.
• Protection: When you really liked the 4e concept of the Defender role, this is your choice. I wish I had more to offer on this one, but I've never had a chance to see it in action.
• Two-Weapon Fighting: Adding your Ability Score modifier to the bonus attack you get from two-weapon fighting makes this style seem like a damage-centric choice, but it's not. It's best used by warriors who are fishing for critical hits (like Champion fighters), warriors looking to tack on rider effects to their attacks (Battle Master fighters), or warriors looking to trigger an additional effect (the Hunter ranger's Colossus Slayer ability or maybe a multi-classed Sneak Attack). The Dual Wielder feat is probably your best option, since it partially helps shore up your Armor Class and lets you use weapons that don't have the light property (which in turn boosts your damage a bit).