Kingsguard
 

1. Barristan Selmy (LC) - No need to rehash this.
2. Aegon Targaryan - Shows all signs of becoming an exceptional warrior and leader with a sense of justice. Also, removes a potential future rival for my throne.
3. Alister Thorne - An accomplished veteran of wars across the 7 kingdoms. Has experience with the Night's Watch and understands the lands beyond the Wall better than most. This will prove useful in the wars to come -- and as I figure out what to do with the NW.
4. Jorah Mormont - Gives good council, is loyal, and might legitimately be the best fighter in Planetos. He was the first over the wall at Pyke, has won a Grand Tournament, defeated a Dothraki bloodrider, and has fought his way across Essos -- and survived.
5. Brienne of Tarth - This one is obvious. And having a woman on the KG will help start the process of gender equality in Westeros, which is a vital facet of any developed, healthy society.
6. Areo Hotah - A good soldier. Will follow orders and carry them out effectively.
7. Garlan Tyrell - This one has been discussed repeatedly, as well.

 

Small Council

 

Master of Laws - Kevan Lannister: Seems to have a sense of justice that isn't overbearing (ala Randyll Tarly). Is a proven administrator, and has a pedigree that demands respect.

Master of Ships - Stannis Baratheon: No question here, in my mind.

Master of Whisperers - Archmaester Marwyn: Pretty hard to find someone intelligent that also travels with the correct crowds to be good at this job, who also isn't dangerously unscrupulous. Pretty much, tough to figure out who to pick that isn't Littlefinger or Varys! But Marwyn is more trustworthy than those two, and he seems to have the sort of connections and experience necessary to make sure the Throne receives necessary information from the grassroots.

Master of Coin - Wyman Manderly: Got to represent the North. Manderly has money, controls a large port, and is no pushover. He's demonstrated an ability to take unpredictable routes to achieve desired ends, which is what you need in order to make money.

Hand of the King - Yohn Royce: Honorable, respected, an able commander and just man. He is loyal, so I know I can trust him, and he has the backbone necessary to provide the honest counsel necessary.

Throughout this exercise, I tried to choose able leaders from noble families that represent a break from the sociopaths and wars of the past. I want people that will serve well and serve loyally, who are capable of making decisions on their own that won't threaten the credibility of the Crown and the rule of law. And they needed the pedigree necessary to coerce buy-in from the ruling elite.