I'll also vote Hunter, with Warlock a close 2nd...
You have to be willing to sacrifice your pet/summon if it means the difference between life or death... Any pet with Growl can draw aggro pretty well, combined with the "Stay" command, you get a quick exit...
The pets get over it, throw 'em some food and they forget you got them killed, real fast... The summons, well, they aren't real...
I do believe just about every class is soloable, but you specifically asked which was "best"... Just my $.02...