I like battlemaster because they can be added post hit.
The issue you face is a clerics 8th level ability, divine strike.... do you care or want it?
The other issue is finding away to beef up your many attacks of the fighter
But channel divinity and maneuvers recharge on short rests, so it shouldn't be a problem there.
I would make this build Fighter 1, then cleric to 5th level for spirit guardians, this is a great spell especially coupled with booming blade.
Half-drow is an option as well, as you can pick and choose what you grab from your parents.
I could see 11 fighter/ at least 5 cleric
rapier and shield is fine