I would go fighter or paladin for 4th ed, multiclassing into cleric. The extra heal would be worth it in my opinion.
On a different note, I think solo campaigns have an advantage that they can be tooled closer to the character, so as long as GM and player are working together, you could have a fun and interesting solo campaign with any class.
A cha-based paladin with high wisdom has an insane staying power. He won't be going down anytime soon. He could also have some decent social skills easily.
Aside from that, I have always found the rogue or wizard as the best classes for solo adventures, regardless of the edition.