So I was checking out GameBanshee's Arcanum site and they mention using empty chests in an area as stash space... just to confirm, you can store stuff in unlocked chests and it won't vanish on you if you leave the area? I hope so, that's going to help a heck of a lot...

Correct - just make sure to not use Trash Bins (or junk barrels), those tend to regenerate/get emptied now and then.
Good bet is to find a warehouse/house/site that has a chest or closed barrel (or something like that) and use it as a dropping off place.
You can use Joachims room in the Shrouded hills Inn to start - the chest there is 'safe' for storage (tested it multiple times :D)

Somebody else mentioned a warehouse in Tarant, the one which you have to clear of rats (east side of map past the fortune teller and brothel), the one i always use to use was the wolf cave. The Tarant warehouse though, since it is so close to the shops is probably one of the better locations to store your stuff.

There's also a small building with a crate in it between Vermillion Station and the Zoological Society in Tarant, next to a steamrail station. The crate has some loot and doesn't respawn, so it's safe for storage.

IIRC down the south theres a rather ill fated ship with plenty of storage space (and swag) which works rather well.

The blacksmith in either Dernholm or Shrouded Hills also has a chest you can use, just inside the door. You get access to it after completing an early mission, something about collecting payment for a repair the blacksmith performed.

If I remember right, there's an inn somewhere with a chest in the room that you normally get. I think it's in the town where you pick up the dog. It's a bit out of the way, but I played a Mage with the Teleport spell. I suppose a tech character would want a central location or one on a rail line and the Tarant warehouse is good for that.

The Warehouse has the advantage, that it has 4-6 Chests/Crates, don't remember the exact amount right now. It is close to the Wise Woman and the Fence in Tarant and there is a Subway Station within a Block with which you can travel back and forth within the city.
It is, however, not the most beautiful home in Arcanum. I bet you can "aquire" a nice little landhouse by making the former owner "disappear".
It is strange, that Troika didn't programmed in the opportunity to buy a house. That would have been cool and it wouldn't have been so difficult. I mean, you could even buy one in Divine Divinity.
EDIT: Thread Grave Digging ftw -.-

You can, for a very large sum of money, late in the game you can buy the Bates Mansion.
The easiest way to test if a chest in Arcanum is safe is to dump some junk in it you don't need, move away from the area by at least 3 screens (further the better) and advance game time 3 days. If the stuff is still there when you go back, its usually quite safe.
The trouble with the Warehouse in Tarant is there are a couple of respawning crates right near the safe chests. Proper metal chests are usually fine.
As for Divine Divinity, you can set up camp pretty much anywhere in that game because chests can be dragged around and used wherever you like. A popular site is by the Magincia teleporter. I leave a teleport triangle right by that world teleporter for the whole game. Even after I buy the house in Verdistis.

would the chest in the inn at the first town work?

If by the first town you mean Shrouded Hills, then yes. In fact, chests in most (if not all) inns will work; my favorite is the one in Black Root, since it's right there whenever you enter that town.

I don't know about the rest of the towns but BR's inn doesn't seem that much closer than the on in SH. It's also only that close if you're arriving by foot (or I assume teleport) so if you're using the train it isn't that convenient. I haven't bothered to leave anything there so far because it looks like it's in a bit of an awkward location, but I haven't exactly tested whether getting in/out of there by foot is a problem.

So far I'm liking the SH chest the most for its location on the map but it can be a bit of a pain pathing around the river sometimes. I just hope there's somewhere better in the rest of the game because it's certainly not a GREAT place to have to return to for storage.

Yes, Black Root is far and away the most convenient by both foot and spell. From the midgame on, unless you're playing a techie you want Teleportation, if for no other reason than hoofing it becomes more and more annoying. (Waypoints and spiders and Kites, oh my! :p)

And speaking of annoying, that train station ticket vendor dialog gets real old real fast. That's reason #1 never to use the train unless you absolutely have to. Here are a few more:

2) No dogs (or animal familiars) allowed.

3) If you don't walk from Tarant to Ashbury at least once, you won't uncover the "secret" Forbidden Pit with the small pile of treasure.

4) For all three cities, it drops you off in an inconvenient part of town (as you yourself pointed out).

5) It costs 75 coins per passenger, every time. If you have five or six followers, that's a helluva hit. (In fairness, high Persuasion can lower this price, however.)

Back on topic, if you are a techie the Tarant warehouse is probably the way to go: it's convenient to the subway, and there are multiple containers available. (Protip: apparently some of them respawn; best to test them first. The one outside the main warehouse door is the only one I've ever used.)