SPOILERS I guess.
1) STORY
I'd like maybe a little continuity from the previous game but not an overwhelming amount, like I'd want relevant characters and plot lines to continue but I wouldn't want a parade of 'oh its that guy' which inquisition did a little bit. I think the story is sort of hard to predict. Most folks seem to be going with the qunari vs tevinter, but not sure if that is too obvious/a scaled up repeat of the mages vs templars conflict, something they've done for the best part of 2 games. Also given that they've gone at a snail's pace in regards to geographical expansion. Ferelden featured in every game for example, and we only have seen bits of the free Marches,with that in mind I could very much see dragon age 4 being Fereldan/ Orlais/an expanded free marches and maybe Nevarra or anderfels as the new area. Could see Tevinter having a presence in the game, but not sure they'll be pulling the trigger on it being the focus just yet. I'd imagine it will be stop Solas from freeing the wrath of the old elven gods on the world that has mistreated elves in these areas.
2) CHARACTERS
Solas or flemeth becomes the antagonist, which I am fully for because I think this would represent the most 3D villain they would have yet in the franchise, Solas being someone we've seen in the role of friend or more and Flemeth being someone that we have at least got to know partially, now in a darker context. Villains haven't always been the franchise's strongest suit so this is the natural move to go to raise the emotional stakes IMO. I think by necessity the Inquisitor would by necessity have to return in quite a big way due to the personal connection they'd have with solas. Not as the playable character, but maybe as a prominent NPC or even shock horror as a companion, though admittedly that would be a bit awkward storywise with the inquisitor being a big shot and you probably being some nobody.
As for potential characters, I'm open -minded about this and have generally been fine with every batch of companions give or take a couple of people so generally I'm up for anything. That said a couple of ideas
A white knight Templar companion - I think the games have always been a bit little one sided with its portrayal of the templars, although I think Inquistion was an improvement on this front with Vivienne's POV and Ser Barris. That said we have never had a templar companion and I think it would be a good, world enriching move. I guess this could be sort of difficult as in some people's canon the templars are completely K.O'd. but still. Maybe a cool feature might be if you sided with the mages you get Fiona as a companion in the next game, and if you sided with the templars Ser Barris (Othe templar if he died).
Second/third/fourth all the suggestions for a Tal-Vashoth Qunari. Preferably a mage. Would be dope.
Elven God. Because that would be awesome, the elven guy from the temple as someone else suggested would be cool, but I think he can die? He didn't in my play through but I'll bet it was possible.
Wouldn't mind a couple of returning companions, to help with continuity and the sense of world building. I think a returning Morrigan makes sense on account of the whole/flemeth solas situation, but that aside I'd like maybe 1 or 2 less obvious ones. Like Maybe Blackwall or Cole. Or perhaps Sebastian just for the troll value. Tho if I were a betting man I'd probably put my house on Iron Bull coming back.
LOCATIONS
Already sort of went through this, but to add to that Nevarra/anderfels makes sense because I think if memory serves the other dwarven kingdom is on the border of the two countries, so would be a chance to get them back into the game somewhat, as I think the reason they've benched the dwarves somewhat is because the Orzammar level in Origins is maybe the most all encompassing level yet, it covered their history, their social divide, their culture and their politics. I can see why they felt they had nothing more to do there, but kal sharok would provide new opportunities
OTHER:
More death = I kind of missed having my companions potentially die if I did things wrong lol. I liked the Hawke/Grey Warden choice but feel they could have gone further with that kind of thing, particularly as their mantra is to not have many of the companions show up in future games. If a character is invaluable to the plot than sure, but I think it would give levels more bite if companions could die if you hadn't met certain conditions in the mission or in the game prior, or important NPC's. So the people who want a perfect happy ending can get it, but I can also have a more tragic playthrough if I so choose.
Side missions more driven by story than fetch questing = I know there's people who love this kind of thing, but I basically didn't care about almost any side mission I did in the entirety of inquisition that wasn't connected to a companion. You didn't get to talk to the minor characters involved in close-up which meant I think it was hard to connect to their problems and invest in them. I know people love grinding so I'm not saying dont put that stuff in the game, just make it land a bit more for people more concerned with story. I loved most of the side missions in dragon age 2 for example, could care less here.
Wow this ended up super long I apologise