It would depend on the type of paladin I was playing. My personal favorite is a Duelist Paladin with a rapier and an empty offhand, but it requires a DM willing to give my houserules a look. In a more traditional game, I'd go sword and board for a devotion Paladin and great sword for a vengeance paladin.
Definitely great weapon for Vengeance. For Devotion, I lean toward sword-and-board but great weapon is perfectly viable. For the other Oaths, sword-and-board all the way.
There is a sword and board Ancients paladin at my table who is like the core of the group. High AC, boosts saving throws, and gives resistance to spell damage. It would be so much more scary for me if his Charisma was not 8.
Between having your holy symbol on your shield and a free item interaction (drawing or sheathing your weapon), what exactly keeps you from spell casting as sword-and-board RAW?