There's actually no way to directly save/load in this game. Like minecraft, it's more of a persistent world that autosaves in parts as you go, and which you can enter and exit at any time. Partly this is due to the way data will be saved, but also it's from our desire to have this feel like a place you go, rather than a game you try to metagame too much (ideally never trying to savescum or encourage that, etc).
So, all that said, the next character usually won't spawn. Rather you get to choose from amongst some of the npcs you have interacted with in some ways, and you get to choose between them. You then take them over whereever they are at the time got other character died (more often than not, they would be in one of your settlements).
If you are out of characters (ouch), then you'll get one spawned at random somewhere. Haven't decided exactly how that will work, but most likely it will be in some quasi-safe place. In terms of getting back to where you were when you died, the overworld travel system would generally make that pretty straightforward if you were strategic with where you place god settlements and wind shelters. If you're more on the bleeding edge of your known area when you die, or explore waaaay out into the unknown on a long trek, then that's going to be reflected by nature in how long it takes to get back there.
Clever players will store many of their items in their settlements, rather than carrying the world with them at any given time (though inventory will be either massive or unlimited -- the rationale being that already ourr encourage to leave stuff behind because of the death mechanic, and the last thing we want to encourage is returning to a settlement just because your stupid inventory is full. And yes I'm aware of the torchlight dog method, but that seems a bit too easy in some respects. This is a bit more inspired by demon's souls of all things).
Anyway, since you can shape and settle the world to some extent, there's no reason you ever have to be super far away from places you can fast travel to. If you don't take the time to put down wind shelters when you go to a new place, then that will make travel more difficult, but that's your choice to be overly bold, rather than the base way the game works. More on a lot of that soon.