Not super-impressed by bow fighter.
First of all, while I agree that it works by RAW, I think Trip Attack is begging for a DM to slap a "melee attacks only" flag on it for reasons which are obvious. Fortunately, Feinting Attack and Precision Attack also exist.
Yeah...I actually ended up not going with Trip Attack anyway; the 45% chance to trip was just shitty, and I didn't want to calculate what that would mean. Also, it's literally only useful when you're ready to Action Surge. When you're not...I mean...maybe you get one attack with advantage out of it? Gross.
Secondly, bows can't opportunity attack. You're a fighter. One of your big advantages is that you are more durable than the party average, can get in enemy faces and make them attack you, or risk your opportunity attack (which can potentially trip or push). If you can't opportunity attack... too bad, so sad, you don't get this advantage, and the enemies will probably work on hitting your more fragile allies. If you want credit for your durability, better have a melee weapon.
I...don't think fighters need to be the tank? Like...they don't resist all damage the way Barbarians do. They don't have the Druid's Wild Shape to get free 42 bonus HP (twice per short rest).
Like...they CAN play the role of the tank, and if your party doesn't have a tank and you want to play a fighter, sure, that's a good way to build them. They're not inherently any more durable than, say, a Ranger, however. (In fact, of the classes covered so far...Barbarian and Druid have clear tanking abilities, and Priest might be more durable too just because they can put everything into AC without losing much).
Thirdly, ranged attacks have disadvantage at melee. You're not a rogue, you don't have free disengage. Nor do you have saving throw spells like a pinned mage. If enemy(s) close to melee with you, and you don't have Crossbow Expert... what are you gonna do, exactly? Use Evasive Footwork for +4.5 AC against the opportunity attacks, or accept disadvantage. Neither sounds great.
But I did end up getting Crossbow Expert after evaluating going without (Crossbow Expert + Sharpshooter had the most damage...).
Duelling rapier fighter, 2x ASI:
Damage is 1d8 +2 (duelling) +1 (magic) +5 (stat) = 12.5, with 75% hit. If we use Precision Attack we... basically don't miss. 91-94% accuracy depending on if your DM lets you recover from rolling a 1. So... 23 damage with two attacks. 19-20 AC. So... less damaging than the crossbow build, but more reliable, more durable, and can actually tank/defend.
OK...the issue I have with this build is where do you go from here? I guess you use your ASIs at this point on...better guarding (Sentinel) and then tankiness (CON, Heavy Armor Master or Medium Armor master depending on whether you're dex or str based?) Yeah, that works. I will note that if you're focused on damage that there's really no Feats left that both boost damage and let you use the duelling fighting style. Wait...no, I'm wrong, you could get Polearm Master, and then wield a quarterstaff in one hand. (You need to be strength based for this, of course).
In fact, pretty sure that will be better than just getting the stat to +5.
1d6 +2 (duelling) +1 magic +4 (Stat) = 10.5 (bonus attack from Polearm Master will be 9.5). All of this with 70% accuracy (+8 to hit); with precision attack...84% chance to hit assuming you don't bother rerolling 2s or 1s (less than 50% chance to even save you--waste of a superiority dice IMO). So...25.5 damage on average. Compared to...I'm actually calculating precision attack only brings the 75% hit case up to 89%, which is 22 damage.
BUT, you also get extra attacks of opportunity (getting attacks when enemies enter your range).
EDIT: ah, you meant for this to be a dex build. Well yes, no Polearm Master then.
Greatsword fighter. Your armour is more expensive, and you have -2 accuracy, but you still have opportunity attacks and you do hit harder when you hit. Without GWM, first, that's... 20 Str. Greatsword with the damage boost is 8.33, so that +5 +1 = 14.33 per swing, 28.67 for two, 91-94% accuracy. So... 26-27 or so. Beats the crossbow build in practice. 17-18 AC depending on if we allow plate. Lower initiative than Dex builds, stealth disadvantage, Dex checks/saves are more common than Str ones for what it's worth.
Greatsword fighter with Great Weapon Master? Base hit drops to 70%, if you fish it's 45%. This is lower than I'd like, even with Precision Attack, which makes it like 60%. Still, 23.33 per swing = 46.67 * .6 = 28.3 or so... it's there if you want it.
Again, I'm calculating that with precision attacks it only brings it up to 89%, so 20 str GWM is looking at 25.5 average damage per turn.
18 STR Precision attack with GWM...ok so...4+1+3 = +8 to hit. Down to +3 to hit. Don't roll below 12. On an 11-7 precision attack can help you. Below that...I probably wouldn't waste a superiority dice because it has a more than 50% chance of still missing. 64% chance to hit. So...30 damage on average.
That said, if you're looking for an opportunity attack machine with a two handed weapon, I think what you want is Polearm Master and smack people with a Hatbot...I mean Halberd. Compared to the Quarterstaff calculations above...it's d10 instead of d6, so +4 damage (+3.4 after accuracy). 29 average damage. Reach. And Reach on opportunity attacks so you zone out more of the battlefield, and more stuff that triggers opportunity attacks. You can also combine this with GWM if you feel like it (Hatbot...I mean Halberds are a two handed heavy weapon. 59% accuracy even after precision attack. (3+1+10)x3 + 1d4+2d10 = 42+13.5 = 55.5. 32.5 average damage. Eh nah, as tolerant as I am of a little extra variance, that's only a 10% damage increase, doesn't sound worth-it.
So...if you're looking for an opportunity attack zoning tank, I think you want Polearm Master and +2 STR. (Unless you wanted to REALLY focus on opportunity attacks, and then you go Polearm Master and Sentinel).