The easiest one to master and the most reliable overall due to the available toolkit has to be Prot Pally.
Unless scaling is messed up real bad, we're most likely always will be able to solo with it as they have so many tools that can't really be taken away by level caps as these tools are such a baseline it would make no sense.
Resto Shaman, while not having been as consistent is both always at least viable and currently plain OP.
And to round off Bear Druid is also reliable, has excellent utility and while it has been a tough to master spec before, it also has tools that make it so it will always be more or less viable.
That would be the big three but as of now Blood DK is excellent and has been viable since we got them (even if a risky option in SL), Priest are wonderful as long as they have their damage reducing passive, pet classes always find a way to work, Monk is also surprisingly consistent and has been what I'd consider the easiest class to learn how to solo with in DF (you just had to do your damage rotation and you'd both deal damage and heal without having to think about it which could be amusing), Warriors are also good as long as they have a proactive heal, DH are Prot Pally level except a bit less sturdy and reliable while being a bit harder to learn for the first time and rogue/mage is basically asking for a bad time.
Honestly with buffs/nerfs, toolkit changes and scaling changes we don't know what will be the best tommorow and it's so easy to get at least a semi-BiS gear with all the warbound stuff now (honor for instance) that you shouldn't really worry about it too much.
That said Pallies are a safe choice, Shamans not far behind and Druid/pet classes always find a way so if you want a twink that'll be able to handle the previously mentionned changes these 5 are a good bet.