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I see four options.
1. You get one single mon from the wild area.
2. You get one each time you "have to" visit the area for story, which I think is like 2-4 times
3. You get one for each of the major divided areas. The lake area, the bridge area, and the desert area.
4. You get one per sub divided area. These divisions can be seen on the map.
As for encounters, I'm thinking you get random encounters only. You could also do whatever you see first.
Personally when I nuzlocke it ill be doing one per sub divided area, random encounter. Fishing is allowed.