Well, there are no real priorities here -- the game simply loops over all cities of all the potential trade partners and compares the respective trade profits.
The order during the looping is determined by the IDs of the players (= the order in which they appear in your F4 foreign advisor screen) and the respective order of their cities (= the order in which they were founded or acquired = how they would appear in their F1 domestic advisor screens).
Cities checked at a later point need to yield better trade profits to push back cities that were checked in the beginning. Thus, the human player who normally has the ID=0 (may only be different in scenarios) will usually have a high number of "outgoing" trade routes = a lot of AI cities will have trade routes with the human cities in a balanced game situation, since the human cities are checked first. Therefore the human's Exports-Imports statistics in the F9-Demographics screen will often be negative, but this is rather irrelevant economically.
But it is not completely irrelevant concerning another game concept: Espionage!
Espionage missions get a discount on their
-cost if the target city has an outgoing trade route to a city of the spy's owner. So the human is at a slight disadvantage because missions against him will be a bit cheaper than against other players
on average.
Note that the loop order in which your cities "grab" their partner cities is optimized. As a first step, all your cities are sorted according to their inherent total trade modifier (= function of city size, connected to capital, harbor, but not customs house). Then each city determines the best available partner cities and establishes the trade routes.
--> In a situation where you move your palace to one of your cities that you founded or "acquired" at a later date, make sure that this city has the best total trade modifier to grab the most lucrative trade routes first in order to maximize the benefit from +50% bureaucracy-bonus on
. Build a harbor and grow it bigger than any other harbor-city preceding it in your F1-screen.