Starting with items
Most classes are well balanced against each other, but not items.
Belt of Storm Giant Strength
An item that truly deserves the Legendary rarity. +9 to your attack and damage rolls is huge. Of course it is only +4 if you already have Str 20, but why would you, when you can have this item instead.
Now we just have to find the class that can make the most attacks with this item.
This is only rare, does not require attunement, and with the right feat (Polearm Master) enables an additional bonus action attack.
A 17th level Fighter can make 3 attack per turn, with Polearm Master it is 4. They also get the Great Weapon Fighting Style.
So the base damage without spending any renewable resources is 69.9.
Only 3 attacks per turn with with Polearm Master, but in exchange they can add 1d8 with Improved Divine Smite.
This is not enough however to compensate for the lower number of attacks.
A Pact of the Blade Hexblade can attack 3 times with Polearm Master, but in exchange they can add their Charisma with the Lifedrinker Invocation.
They are even behind Paladins, while unable to wear heavy armor, and have fewer HP.
&Fighter &Paladin &Warlock \\
Weapon &6.3 &6.3 &5.5 \\
Strength &9 &9 &9 \\
Magic+3 &3 &3 &3 \\
Lifedrinker &0 &0 &5 \\
Improved Divine Smite &0 &4.5 &0 \\
Secondary Attack &3 &3 &2.5 \\
Attack/action &3 &2 &2 \\
Sum &69.9 &65.1 &64.5 \\
Great Weapon Master
Against ridiculously low ACs, and when you have advantage.
For out-of-turn attacks, but competes with Polearm Master for your reactions.
You did not give us number of rounds between short and long rests, and target AC, so it is basically impossible to calculate with renewabale resources, so I will just list them without any numbers.
Most of your damage comes from static values, will not be doubled on crits, so Champion is not great.
A Battlemaster can use the maneuver Ripost (again, competing with Polearm Master for your reactions), Trip Attack and Precision Attack to increase DPR.
Divine Smites are great, but they only come back on a long rest.
The Holy Weapon spell from XGtE might also be good.
Probably Oath of Conquest iis the best option for you.
Hex looks good on the surface, but you have to sacrifice your bonus action attack for it. That one does 19,5 damage, so you need 6 hits with Hex to come out ahead. Hexblade's Curse is a bit better, you only need 4 hits. Eldritch Smite is a great invocation, but 4 slots per short rest. 20d8 per short rest sounds great, but turning 6 misses into hits with Precision Attack (Battlemaster Maneuver) is actually more.
Pact of the Blade, obviously, the Patron matters much less, probably Fiend and Hexblade are the best for your purposes.
You only care about Strength, and it comes from a magic item, so you can pick any race, Ability Score Increases do not matter.
Constitution and Wisdom are probably the second most important abilities because of saves, so I pick Hill Dwarf. It even gives you 17 HP.
4 Polearm Master
6 Great Weapon Master
8 Resilient (Wis)
12 +1 Con +1 Wis
16 +2 Con
Legendary: Belt of Storm Giant Strength
Very rare 1: +3 Glaive
Very rare 2: +2 Full Plate
Rare 1: Cloack of Displacement
Rare 2: Neclace of Fireballs (against mobs)
Rare 3: Brass Horn of Valhalla (against mobs)
Uncommon 1: Winged Boots (against flying enemies)
The rest does not really matter.