Note that this is a bit retroactive for me. I don’t really have the GMing energy I used to. Also please don’t assume I think I always get it right; I know I don’t.
I found it useful to write up a paragraph or so about each game I’d be offering to get my own thoughts in order. If there are multiple potential GMs, so much the better to compare offerings side by side. (Even for in-person groups I always set up a mailing list so that we can discuss things like this while not actually in the same place.)
I want the players to feel enthused about whatever they’re playing, so I like to give them options. Like the thing in Trail of Cthulhu where you’re invited to come up with a character motivation for going back to the horror, even before play begins, I think having made an explicit choice helps to increase a player’s feeling of involvement.
Of course I’ll also entertain suggestions for tone or emphasis. I may have my own vision for the game but again I want the players to be involved. And absolutely there will be a session zero - in fact for me it’s more like a session zero plus session ½, because I mostly play games with fairly involved character generation. For example at the start of the Bayern campaign (audio on this site) we were talking about the setting, and the sorts of character who’d fit on this mission, in between the actual mechanical generation process.
For GURPS I go further and treat the first adventure as a “pilot episode”. I try to make that as much like my long-term vision for the campaign as possible, and if players feel they want to tweak or even replace their characters afterwards to be a better fit, that’s just fine.
When it’s the same group that’s going to be playing, whatever the game, it’s trickier, as @jfs says. I’ve known games clubs that worked on a 6 or 12 week cycle: every short campaign would end at the same time, and players and GMs would shuffle around into the new ones that appealed to them most. But while I like short campaigns a lot, I wouldn’t want that to be my only gaming.
As a roleplayer and boardgamer, I look at a four hour convention RPG slot and think “I could be playing multiple boardgames in this time, most of which I know I’ll enjoy, and if there’s one I don’t it’ll be over soon”. I’ve had some very good convention games but I do find I’m getting risk-averse.