Decisions, decisions...

[Undyne]

Don't think about their powers. Think about what stories you can build with them. Otherwise you'll do what I did with my alt and switch when the novelty wears off.

This. Exactly this. I have so many stories and ideas planned for Trixie it's crazy. An entire notebook just for her.

That does make sense definitely, although since I'm not yet deep enough into the Omniverse and its ongoing plots it would probably have to be based on the character and what they bring along, rather than their potential interaction with the Omniverse.

The Emperor, the Witch of Izalith and Nonon probably have relatively little potential in that regard:

The Emperor may start a campaign against Diablo, but considering how there's a ton of more powerful individuals than him with the same goal (Aragorn and Tyreal to name the most prominent ones)
The Witch... she'd probably be happy that she escaped Lordran which was going to hell. I'm not even sure if she would fit into the whole Omniverse.
Nonon Jakuzure might wind up being a pure-Dataverse character, rushing a base with an Upload Terminal and living her life in the interwebs from there on But, I don't think that'd be very fun.

As for the other characters...

Garrosh probably has the most story to bring along. He'd build up a Horde faction in no time - though being a hothead with little strategic thinking (IMO) things might get derpy - and he won't be doing many quests since he submits to nobody. The problem remains that in terms of abilities he would be very similar to Alexyana so he might be a bit boring to play after a while.
Artorias would have something. Perhaps he'd consider Diablo a threat similar to the Abyss from Dark Souls and thus prepares to do... something. A wandering knight style of character.
Tassadar, I'm not sure again. There are no direct antagonists to his character in the Omniverse unless Kerrigan zergifies herself, which I doubt will happen, or someone makes a Zerg character of their own. It's also definitely gonna be a "serious" character which may take some of the fun out of him.

I'll reconsider the list for now The first three I think I'll actually take out and instead add in someone else - I'll have to spend some time pondering over this. Then again I'm still over 1500 OM away from even being able to submit a second character, so it'll take a while before I got the option.