DEX based fighter is certainly a viable option.
1 thing that people should keep in mind however is that heavy armor has a STR requirement. You could use medium armor at a pinch but some of the endgame heavy armors wouldnt be an option if you keep your STR to low.
5e armor is largely a choice of flavor... Light Armor, Medium Armor, and Heavy Armor all get to about the same AC.
Studded Leather 12+Dex, 17 assuming maximum Dex.
Halfplate 15+Dex(2), 17 assuming Dex 14+
Plate Mail 18
Natural armor and mage armor are similar:
Natural Armor (Draconic Sorcerer, Lizardfolk) or Mage Armor - 13+Dex, 18 assuming maximum Dex
Unarmored Defense is a bit higher:
Barbarian or Monk - 10+Dex+Con/Wis, 20 assuming max Dex and Con or Wis depending.
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Going into other in-character options, Medium Armor Master feat can get medium armor to max out at AC 18 before magic.
Dual Wield can give +1 AC
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Going into gear options, Shields can get armors (including mage and natural) to 19 or 20 AC and Barbarians to 22 AC... monks lose AC for using shields (which is a bit silly, but okay)
For magical enhancement
Cloak of Protection, Bracers of Defense, and Ring of Protection eat up all three Attunement slots for +4 AC
Shields and Armor can get up to +3 and don't take attunement for pure bonus
The Defender sword can give a +3 AC but is an Attunement slot
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It's reasonably possible to get to high AC numbers with all the various styles, though Monks, Mages, and Natural Armor get high faster, but cap out a little lower due to lack of enhancement bonus. Barbarians are a bit of an exception due to their capstone. With protection items, a shield, and max Dex and Con they can hit 31 AC. Heavy armor can hit up to 30 AC via +3 enchantments and protection items. Mage Armor can get up to 23 with Bracers/Robe of Archmagi/Ring which can be boosted to 27 with Shield.
But the types of non-AC enchantments that come with Light, Medium, Heavy, and Robes are all very different.
So while all characters that make an effort can get reasonably high AC (and in practice they're likely to diversify more) the different lines have different side-benefits. Glamoured Armor by standard is Light Armor, for instance...
Of course, there's nothing preventing a group from making a unique suit of glamoured full plate, but the full plate types are less likely to get use out of that...
