For strongest melee force:
If you're expecting the game to end before level 3, I'd go Human Variant War Cleric with Great Weapon Master.
If you're going to end between 3rd and 5th level, Moon Druid is the way to go. I like the Aasimar for the bonus damage and flight. Moon druid edges out the War Cleric by a hair at levels 3 and 4, but if you don't want to melee it up as a bear, War cleric is also really strong until it is bypassed at 5th level by the Multi-attack classes.
If you're running 6 to 11 levels, I'd go Vengeance Paladin - Human Variant (again for either Great Weapon Master, or perhaps for Sentinel if you want a defense boost and are willing to give up some offense).
If you're going to Run 12 or more Levels, you want a Battlemaster or Eldritch Knight to maximize the melee damage.
However, the class I've had the most fun running as a melee PC was a Hexblade. Armor of Agathys, and Hex are great ways to keep you competitive in damage, and if you get a pearl of power, rod of the pact keeper or other way to get a bonus slot, your extra spell can do wonders. Also, as you can also be very effective with Eldritch blasts, and do a variety of tricks outside your melee capabilities, you won't get that 'slufest boredom' that many melee only PCs get over a long haul. At 11th level, you tend to bloom into something that feels like a powerful spellcaster on top of your melee abilities (which wane a bit at that point).
