I'm going to claw my way to Fighter 3 with my rather unhinged LG Death Cleric. Functionally, that gets me Fleet of Foot, Second Wind and Action Surge and a +1 to AC. Thematically, it gets me Commander's Strike and Maneuvering Attack. But fun-wise, it gives me a some tactical tools, some fiddley bits for my medium armor, Mobile based, melee combat medic.
He's going to be a very tactile, hands-on guy. He'll do all his healing with his hands, and much of his hurting with his hands as well, the hands he used to throttle his undead children. Cure Wounds and Inflict Wounds. Lesser Restoration and Vampiric Touch. Channel Divinity ~ Touch of Death. And the occasional bout of chittering madness.
That's the concept that has yet to meet the enemy. I'll probably end up using almost all my spell slots for cures for the first half of the campaign, because that is what need will likely dictate. So I'll wield a finesse weapon just to be somewhat useful when heals aren't needed or have all been expended. I'll also need a weapon for Divine Strike and the very situational Maneuvering Attack.
Speaking more generally, taking three levels of fighter to get to Battle Master may be a worthwhile gambit in various circumstances. It increases the characters hardiness at Fighter 1, gives him a nova round at Fighter 2, and set of tactical tools at Fighter 3.
Most people dipping into fighter will probably stop at levels 1 or 2, but the Battle Master archetype brings a lot of utility. Battle Master really shines with a Strength build, but it works with a Dexterity build as well. There is a wide enough assortment of useful maneuvers to go either way. And if you enjoy tactical play, the Battle Master is fun.