Alright. Let’s see.
Well the 1st Doctor was a bit of a grouch old grandfather. He’d have no problem being sarcastic with you but he could also be incredibly kind. For him I choose Archie. They’d balance each other out, which is important in DW
2nd Doctor (a personal favorite) could be really scatterbrained. He he came off often as a bit of a buffoon. But he also followed his own rules, hence why the Time Lords force-ably regenerated him. He needs someone who is good with planning and has a strong tolerance for hijinks. I give him Ruby and Granny.
3rd Doctor was the quintessential early 1970s dramatic action hero. He wore a cape and was a theatrical but could also beat you up. He was stuck on earth for a really long time so you need someone who is okay with not going to different place and times 24/7. A homebody maybe? But someone who can get their hands dirty. I choose The Knave of Hearts for him.
4th Doctor (the best. Done) was everything you want in a Doctor–quirky and quick witted and fun and moral and altogether strange. He represents the best of Doctor Who. His companions were also the most diverse, from Sarah Jane who would challenge him to Leela who a student to his special relationship with Romana (1 and 2). 4th Doctor had a lot of flash to him. I think he needs someone who can match that. I choose Rumple for him.
5th Doctor was the youngest Doctor until the regenerated series. He was very human, loved cricket and like a big older brother. He had very few maliciousness about him. I would call him the least dark. Because of that, I think he needs a companion who is a bit spicier. Someone who can poke and prod him into action. I choose Regina for him.
6th Doctor is often labeled as the evil doctor, but really he was very egotistical but still knew his duties as Savior of the Universe. He could be violent and harsh. But he never faltered in his protection of the universe. I think he needs someone who could temper his more harsh tendencies. I choose Snow and Charming for him.
7th Doctor was more of the professor type. His main companion, Ace, was like a beloved daughter or student to him. I think he needs someone that he can mold. I choose Henry for him.
8th Doctor was full of life. He was fascinated by the stars and life and shoes! But he was also born in blood and battle and died in blood and battle. He made hard choices. He had a sense of honor and dignity and strength. He loved doing the rescuing thing. I choose Hook for him.
9th Doctor was a troubled soul with too many bad memories. He wanted to loose himself. He wanted to get away from it all and never face his past. He was a runner. He was haunted by the war and his demons. I choose Neal for him.
10th Doctor as a new soul. He was the lonely god who had lost too much but could never forget them. He knew he would always loose those he loved because that was his fate. He felt his years with every breathe. But that didn’t stop him from being a hero. It was a hard path, but he knew what had to do. I choose Emma for him.
11th Doctor was older than his years but chose to behave as a child. He wanted to find delight in the universe again because he forgot how to see it. He formed close bonds to those he chose to protect and at became unhinged at the idea of loosing them. I choose the 7 dwarves for him.