This is a toughy. I like each Doctor for different reasons. But if I had to pick I would go with Eight. He seems like he's a nice balance between all of the doctors. He can be inquisitive, distracted, jovial, wise, and serious, but also knowledgeable about things beyond human understanding.
As for companions, that is an equally tough choice. So again if I had to chose, I would go with Ian, Donna, and Jamie. Ian and Donna would be the responsible ones keeping me and Jamie out of trouble, while The Doctor asks himself "Why did I ever take these bipedal apes on?"
That being said, ask me again tomorrow and my answer might change.