My favorite's the Elite Scavenger Hunt. I'm good at recognizing the items after all these years, and getting Gold gives 16 medals. I'm also fond of the Ore Hunting tour. I'm pretty sure Gold on the Elite tour gives 20 medals. Playing with friends also gives an extra few medals, too.
Hide-and-seek is the most fun tour to get medals, as for getting a lot of medals, I do the tuna tour since it gives 20 medals a pop(as long as you get 10 tunas already, you're guaranteed to get a gold).
I used to really like the ore hunting one. On Elite, I would finish in 3-3.5 minutes, earning 15 medals, for a rate of 5 medals per minute (at my best).
However, I found that I prefer the scavenger hunt one. On normal, I finish in 2-2.5 minutes, earning 13 medals, for a rate of 7.5 medals per minute (at my best).
I've never tried the hard resource-based ones that give 20-25 medals per, because I really suck at fishing and bug catching, and mediocre at diving.
I can't remember which tour was calculated to be best medals/minute, but I always did that one. And the tuna one. But damn that gold medal is so hard to get.