You only need one level in Warlock for Hexblade and Booming Blade, unless you really want the short rest spell slots, in which case you'd take 3 levels to make sure those are second level spell slots for use on Misty Step, Darkness, or Mirror Image.
6 in Paladin is good for getting your extra attack and Aura of Protection, but you can get away with 5 for the extra attack on its own if you don't have a melee-centric party since the aura range is small.
At the leanest, we're currently at 6 levels, let's take a quick look at the two other Charisma classes and see what they can offer:
Sorc
3 levels gets us 6 spell slots, 2 metamagic options, and some whatever spells
Bard
3 levels gets us College of Swords for the very fun attack actions and 6 spell slots to use on smites.
For a melee Charisma character with some casting, I'd recommend:
1 Warlock (Hexblade, Booming Blade)
5 Paladin (smites, extra attack, and a feat)
4 Bard (college of swords and a feat)
And do whatever you want with the remaining 2 levels, I guess. Fighter for Action Surge or more Paladin for aura and a subclass feature at 7.