There are differences when the park is busy and there are more people playing the game:
1. After you complete your first mission, you will not get the option of picking another country to complete another mission -- you will be instructed to return your cell phone. The cell phones get put in specially marked drop boxes that are located in each country.
2. There will be other people standing at each specific spot while you're trying to complete your mission. You might need to wait a bit so you're not playing your message while they're playing their message or you might even need to wait if there's something that you need to touch and interact with. It's not just the people that are playing the missions that will be in your way though, I don't think that completing the missions would be that much fun if the country that you're in is jam packed with people. The mission requires you to go to about 5 locations in a country often back tracking and criss crossing.
When you sign up for a mission, you can pick what country you want to go to and the CM will assign your cell phone for that country. You have about 20 minutes to get to that country to start your mission. If you wait too long to start your mission and you don't ask for more time, your cell phone might time out and you'll need to return to the sign up kiosk and get your cell phone re-programmed.
After you get to the country that your mission is, you'll be instructed what to find. You'll be shown a picture that corresponds to something in the country -- it might be the picture of a shop, a display cabinet, a landmark. You need to go to each spot that is indicated and then follow the instructions. What you need to do at each location varies: often times you will activate a display. Sometimes you will be given a secret code that you need to enter into your cell phone (Mexico). The fun part of the game is that the displays or landmarks are not marked in any way that they have something to do with Agent P -- it really is like you're completing a super secret spy mission.
I don't think there is one "best" country. Each country offers something different -- they all seemed fun to my 9 year old son. I didn't play but I've watched him play all of the Kim Possible missions and all of the Agent P missions -- the interactive stuff that occurs with each mission is really fun and surprising. It definitely was addicting for my son so you might want to have a talk with the kids before hand if you're only going to let them do one country so that they're prepared. We live here and have annual passes so time wasn't a factor for us. I actually enjoying taking a rest in the country and letting him run around the country completing the mission. I think it really is geared to kids 5 - 12 years old.
If you have more than one kid playing, I would still just get one phone and share the mission by taking turns. Everyone can still listen to the audio and read the subtitles with one person holding the phone. If each kid takes a phone, be aware that you all won't be going to the same locations in that country because the locations are random. 4 or 5 people hovering over one phone probably isn't good either and would get frustrating -- maybe break up into teams and just have a meeting place for when you're done with the mission.
You need to show one park ticket per cell phone when signing up for the first mission.
Here is a link with more information:
https://disneyworld.disney.go.com/attractions/epcot/agent-p-world-showcase-adventure/
But it's good to know that ahead of time so you're not surprised!
