Which is a better early game choice for a Stealth/Nonlethal character, Agility or Possession?

First of all, if you pick up all the runes, you should be able to grab Blink II, Agility I and Possession I by the end of the first mission. All three are enormously useful, however, within that first mission, I'd have to say the most valuable pickup is Blink II. You didn't mention it, but it really is the single most valuable skill I've found for stealth runs. After that, choosing between Agility and Possession is mostly a matter of taste. I'd favor Agility personally, but that has more to do with my fondness for blink spam and distaste for using Mana on anything else than it does to do with any difference in the usefulness of the two skills, and you can easily grab Possession II quite early on in the second mission, where I did find it pretty useful.

TLDR: If playing a stealthy, non-lethal character, better focus on getting Possession II than Agility II first. Possession has better advantages for that character type than Agility. Main advantage: Stealthier routes that are only passable with Possession.

I'm currently playing a character like what you're planning - stealthy and does not kill anyone (except animals, if needed). I currently don't have Agility I (or any other natural, non-magic ability), and the magic abilities I currently have (in the order I got them, and also in the order I frequently use them, most-used first) are: Dark Vision II, Blink II, Possession II, Bend Time II and Devouring Swarm. I just finished The Flooded District. (Edit: I have now finished the game in a stealthy non-lethal fashion without Agility.) I would say that Possession is better than Agility.

The main advantage of Possession to me is, that there are routes (most of the time, with less exposure to NPCs/creatures) that you can never access without Possession: i.e. small vents that can only be accessed by rats and/or hagfish. This makes it very useful for a stealthy approach.

Another advantage of possession is that possessed humans can pick-up items, interact with items (disable security devices) and pass through Arc Pylons and Walls of Light. You also conveniently appear at the back of the human you possessed once the Possession effect has finished, making for an easy non-lethal takedown. If you'd rather not risk enemies finding a body, or getting an unconscious body eaten by rats, humans will be disoriented after they are possessed, giving you time to hide.

Possessed animals are fast, can fit in places humans can't and can be possessed much longer than humans (good for scouting). With Devouring Swarm (summons a swarm of rats), you will always have a body to possess (that's a rat body).

Mana was never an issue for me, even in missions that have few mana potions (Piero's Spiritual Remedies). What I did was try to equip bone charms I have that have mana and potion-improving effects like Spirited II, Twist of Fortune II, Spirit Water, etc. This so I wouldn't worry about mana running out (you won't get much potions on a certain mission). Also, even if without mana-improving bone charms, and if planned correctly, you won't need to use Possession repeatedly to the point that you run out of mana and Piero's Spiritual Remedies (might need to use the quicksave/load keys there).

I don't really see how better jumping can help someone playing a stealthy non-killing character, considering that even Blink I can take care of the need for the extra jump height, for those hard to reach places (for everything else, there's Blink II). Blink I and II also does not cost too much mana. Also, blink-jumping can still be done even without Agility. I can see how blink-jumping + Agility is needed for a character that kills - stealthy or otherwise, though (easier escapes, better points of attack, etc). I haven't seen a route that can be accessed only through Agility, but there are routes (mostly easier) that can be accessed only through Possession.

In conclusion, Possession is way more useful than Agility if playing in a non-lethal, stealthy fashion. You and can rely on Blink for those hard-to-reach places, instead. Though, Agility could be useful with a character - stealthy or otherwise, that allows killing.

^{Also, this shouldn't be an issue once you got enough runes to get both Possession II and Agility II}