I think starting with Medoh and ending with Naboris is the best. Medoh first because the champion's power opens up your paths of traversal even more. And Naboris last because it is the most challenging (and interesting IMO) out of the four, so you get to work up to something.
If I was to give just one recommendation, I'd probably take them in the following order:
1) Medoh - because of the champion's power aiding your traversal
2) Rudania - because the campion's ability will further aid you when encountering enemies
- also, these two are the easiest out of the beasts, and have the easiest boss fights
3) Ruta - because by this point the champion's power actually gets more worthwhile (in the beginning you get essentially the same effect with fairies) and the dungeon/boss is more interesting than the previous two
4) Naboris - end on a high note, the most interesting dungeon and most challenging boss fight, and because the Yiga attacks ramp up after doing this quest