Adventure Ideas For an Introduction to Planescape

You could start off in Arborea and have a raid conducted by a group that retreats to Ysgard. The group might be native Ysgardians, members of a rival pantheon or from the Seelie Court. The focus of the adventure would be a stock and standard "Retrieve the MacGuffin". This gives you a chance to highlight what it takes to move between planes and how each of the planes is different (both in look and in philosophy).

Personally, I think you might be on a better track sticking with Arborea or Ysgard. For someone new to the game, a place like Ysgard provides a modicum of familiarity (assuming that the group knows a little bit about the Norse pantheon) but still allows for some unworldly aspects (e.g. floating earthbergs, bariur) and a little bit of danger (e.g. non-evil people trying to pick fights)

Here are a few random plot ideas (several undoubtably stolen from others) that I have jotted down for Ysgard (I didn't have much that was good for Arborea):
-Bariur males get their spouse during a yearly race. All the single rams have to chase the single ewes. If the ram catches the ewe, they can be wed. If the ewe outraces the ram, the ram must pay geld. One less-than-swifty bariur ram is deeply in love with a feisty ewe (who is fleet of foot and probably won’t let him win her just out of pity); and he has a fleet-footed rival (whom neither he nor the ewe like). PCs asked to help (could also be used to cover a lot of scenic terrain)
-Region of the World Ash is corrupted. There is a dark spot in the wood and the surrounding wood visibly ripples. Ratatosk are acting nutty (aggressive) due to the corruption, travel to (and hence battle with) other islands hindered as a result. PCs must help resolve this problem since natives can’t combat the ratatosk
-Retrieve a magic item taken in a giants' raid
-Get quality magic from the reclusive dwarve smiths
-Competitions on Ysgard to see which band is the bravest, most cunning, etc. “Enter the Dragon” type competition brings in visitors across the planes to find the best fighter
-Criminal has escaped to Ysgard and been befriended by berserkers. Mercykillers (or the police agency back in the Prime) want him captured but how do you fight off a troop of hardened warriors that always come back to life? How do you convince them to “betray” their brother-in-arms?
-Ysgardians find a displaced unit of samurai in Ysgard. They relish these excellent opponents but the same rules don’t apply to the Oriental visitors so they are wasting away. Diplomacy is needed to stop the over-eager barbarians
-Demon in Ysgard is torturing, but not killing, several petitioners. PCs asked to help in the hunt. Remember, a petitioner has to die fighting to return so the prisoners must be freed before being killed
-Ysgard/Outlands: Slaad Lord seeks to look into the Well of the Norns to see his future. As he is the embodiment of pure chaos, he is hoping the Well will fail, be destroyed, empower him, etc. PCs asked to deter/distract him (May not be great for an introductory adventure but the Well of Norms might make a good McGuffin for something you design)
-Periodically, Odin must delve into the “Odinsleep” that reconnects him with the chthonic powers and rejuvenates him. During this time, rulership of Ysgard passes to another god. This is a favorite time for giants or other foes to strike. (Again maybe not ideal for an introductory adventure)

The one modestly interesting idea (IMO) I had for Arborea was taken from "Tales from the Outer Planes" (at least I think it was from there):
-The trickster Hermes (diguised as a goatherd) lies and tells the PCs that the only way to leave the plane is to get express permission from Zeus. He also says that if they can bring him a reluctant nymph, Zeus will be glad to grant their wish to leave. Hermes then makes a bet with Apollo as to whether the PCs will succeed. So Hermes, Apollo and eventually Hera will become involved in trying to indirectly (as they don't want to get caught "cheating") affect the results.
This can make the PCs visit a lot of locations (especially if you want to complicate things - e.g. the nymph first wants the PCs to get her a beautiful coral tiara from a triton who in turn wants something else perhaps from a non-Greek like a Sensate, an eldarin or a elfin power), can expose them to various dangers from Greek myth, and can provide an out (a literal deus ex machina) if the PCs are in danger of dying (Hermes might be capricious but he's not cruel)