In Game of Thrones the assignment of each player to a house has a drastic impact on the way the game plays out.
What are the different ways to assign houses to players, and what are their advantages or effects?
Where a player sits around the table has little influence on the turn order of the game. Straight out of the rule book, on page 7 (emphasis mine):
Your house position on the Iron Throne influence track abstractly represents the strength of your claim to be king as seen among the minor nobles, knights, and people of Westeros. In the game, the Iron Throne Influence track determines the Order of Play, and the highest bidder also gains control of the Iron Throne token after all the bidding is resolved.
The turn order is determined by the Iron Throne track, so it changes over the course of the game, and the player that starts at position one of the Iron Throne track is determined by your starting House. If the concern is House picking, that is also covered by the rules on page 3 (emphasis mine):
6) Each player now randomly draws a House Start Card to determine which house he will control for the rest of the game.
House draw is supposed to be random, so following the rules here should prevent any shadiness among players. Randomization shouldn't favor any one player, so this should solve any problems with assignment.
As such, feel free to sit anywhere around the table you want, as it won't impact the flow of the game too much. Although sitting closer to your starting location on the board is always a good idea so you don't have to reach across the table for everything you do.
Positions are assigned naturally, according to where people happened to be sitting when the game starts.
In the setup phase of the game, people will have sat at the table to chat, help set up etc, or arrive later and sit without regard to the board game dynamics.
Announce the start of the game and tell people that's who they're playing.
Is an interesting twist on random.
People may be unhappy about the position they get.
If people are aware of the seating process they can influence their position.