The price for a mercenary is that you need to remove from your deck the amount of cards equivalent to the Mercenaries level which is 6. So if you take a mercenary you more then likely will have fewer cards in your deck then your opponent. But since there are only 2 mercenaries in this set so far and you can only swap out cards that are the same types (mercenary - mercenary, crew - crew) then it's a moot point right now. I am guessing future add on cards will have lower level Mercenaries available in them.
As far as how to determine who gets which mercenary, I assume, since it's not in the rules that you randomly issue them to players in the base game.
Sorry, can you point me to that page in the rules (either online r in the physical set)