(I haven't yet played XIII and thus can't comment on it.)
First, DO the Final Fantasy VII remake. It's basically printing money. Don't touch the gameplay or the story, just prettify the graphics and clean up the script. Then don't do anything else with VII: enough is enough.
While we're at it, let's port some more of the previous titles to the DS.
Now,to the future:
I've always liked Final Fantasy's habit of trying out new and different leveling and ability systems with just about every game, and we should keep right on doing that. I for one love rich, labyrinthine class/ability trees with minimal overlap and more than a few actually useful jobs.
While the level of graphical detail possible today really is totally amazing, I propose we pull back a little on the complexity of character designs, mechanical designs and particle effects. Yeah, they're cool, but too much visual busy-ness actually detracts from the impressiveness of the scene. We needn't go totally retro, just eliminate some unnecessary bangles and zippers.
Combat transition screens will be made as short as possible, if they must exist at all. In games with turn-based combat, we will have the option to hasten or remove battle animations. Let's at least have the option to exert direct control over any or all party members, even if we have some fancy AIs to pick up the slack the rest of the time.
Also: if a character can do something in a cutscene, she can do it at all other times (and vice versa.) If a character is a wall-running high-kicking gravity-defying badass in cutscenes, then his combat abilities will reflect this. If a character must perma-die as part of the story, a reason will be given for why Phoenix Downs and Raise spells won't work.
I think the stories could stand to get darker again. Not "gritty" necessarily, but let's raise the stakes a bit: let's actually SAVE THE WORLD again (rather than stop periodic depopulation or political control.) Also: while I can understand drawing inspiration from Star Wars, we should maybe try getting away from that a bit.
Having stereotypical characters is sort of a problem with Final Fantasy, especially since it had a big hand in establishing many of these tropes in the first place. Attempting to avoid "Serious Spice" "Manly Spice" and "Kooky Spice" sounds good on paper, but strictly avoiding stereotypes usually just brings you around to other stereotypes or outright parody. Not that it's bad to mix things up, but well-used character archetypes have become well-used for a reason.
Rather than trying to hit or avoid tropes, the key here is exploring each character enough to understand WHY they are the way they are. The default solution here is angst: the character's personality is defined by some Intense Personal Tragedy, and while this can be very moving it's a mistake to do it too often. IRL not everyone has a Missing Wife or Dead Sister or whatever, and it feels weird when everyone you meet in a game has some kind of Dark Secret which is the motivation behind all their actions. Sometimes the Arrogant Mage isn't a snob because he's TRYING so HARD to make up for his BIG BROTHER being DEAD. Sometimes he's snotty and entitled because he's spent his whole life being told how awesome he is.
In short, I would try to make the next Final Fantasy less about spectacle and more about substance. The spectacle can still look great, but there needs to be a heart underneath it that we can relate to and care about.