It's a good idea to make sure everyone in the group understands what the point of the game is about, so they can build appropriate characters. Sometimes people go in building "survivalist" characters, which means the motivations also don't fit the genre expectations.
It's also important to remember that the key point of horror stories is some point of understanding. You don't necessarily need to understand all of what the horror is, or how it works (in fact, learning all about it usually ruins it rather than increases it) but there needs to be a reveal and realization of how bad the situation is or a bit more on what's going on. The character who dies in the first 5 minutes of the movie doesn't make a good viewpoint character at all.
There's basically two types of horror story protagonists: the ones running away from the threat, and the ones who keep trying to look deeper, even though they know this is messed up.
Those who won't turn back
The latter characters are driven by near-obsessive motivations. Movies like Pi, Pan's Labyrinth, and the Ninth Gate are pretty good examples. Some good potential motivations:
- "I must know the truth, all of it."
- "This can't be real. I'll keep digging deeper until I prove it is all made up."
- "I've always had a theory about the deeper truth, this is the only way to prove it!"
- "One of my friends died pursuing this, I swear I'll find out WHY."
- "I will stop this, all of it. It must never be allowed to rise again."
Now, there's a reason these kinds of characters generally are loners/sole protagonists - and that's because if you put too many obsessed characters together, it just looks real weird. Or, maybe, at that point, you've basically formed a cult. (Ironic, especially in a Chthulu mythos...)
Normally, what you can do is have one or two very driven characters, and the rest of the group is support staff driven by other goals.
"Professor Irwin is brilliant, and I can't say I understand much of what he's going on about, but I know that if we complete this expedition and bring back the famed W'skselth statue, my name will be famous!"
"My brother always has had grand ideas, but he's never had to go into the real wilderness. I saw what happened in the war, I've had to drink water out of mud puddles and kill wild dogs for food. He's going to need me."
Now, the thing to realize when you do this, is that characters with differing motivations along these lines will reach the point where they will be pulling in different directions. One person wants to keep their brother safe, another really wants to just get the statue, another still is trying to spend time studying the inscriptions on the wall... the biologist wants to take back a sample of the monsters...
In horror stories, this is a great chance to give character development, to show who the personalities are, and to set up spaces where people fail to cooperate, or act together in ways that create opportunities for things to get worse.
Most roleplaying games, on the other hand, are pretty crappy at the play structure that comes out of it, though. You end up with people arguing, and then the party falls apart without much entertaining value to come of it.
Two system based things make this work better - rewarding players for roleplaying their character's motivations brings the focus of play on those, rather than a "mission", and second, having a set of rules for social conflict. When the group is pulling in different directions, being able to get people to agree on some level through convincing, bargaining, or threats, allows for more functional stories and mirrors the kind of fiction it draws from much better. Without these things, the group tends to either splinter or have no real goals at all as individual characters.
"Campaign" may not be the way to go
Most horror stories don't last a very long time. High danger threatens quickly, and so most stories end quickly. And characters usually don't last very long in these situations without reaching their physical, mental, or emotional destruction. (Be sure not to confuse action-supernatural stories with horror - those have way more control and agency to the characters involved.)
It makes sense to look to resolve one horror scenario. A campaign might make more sense to introduce new characters each scenario or event. Maybe they have connections to the previous characters ("My uncle retired after that expedition. He was rich, but very eccentric. I just got a letter from him, he was in ill health and had something important to tell me...")
You might have a single character who gets pulled back in, years later, forced to act to deal with the problem. ("That's no murder! I know that sign! They didn't destroy the book! The University lied!")
You'll also notice that the reward system of character growth and improvement is not particularly well suited to disposable characters this way.
It can help to have mechanics that drive pacing a bit. If you can guess how close your character's story is to ending, you can roleplay in a way that brings the issues and their motivations to a climax. (Maybe this is too metagamey for you, I find it makes great games and doesn't require a lot of thought.)
Games like My Life with Master, Polaris, Thou Art But a Warrior, Poison'd, 1001 Nights, Grey Ranks, Bliss Stage and so on do great at this. The closure mechanics either force a character to an endpoint of the story or the whole story itself. What a lot of these games do, that Call of Cthulhu doesn't do, is that the endpoint gives the players some aspect of narrative power when they hit their endpoint. It's really quite satisfying to build up your character's eventual doom/damnation/death and finally describe it in an emotionally satisfying way.
These mechanics also tend to work very well in horror because you can make sure to reveal key horror elements before all the characters die/go mad/etc.
If the players have set up their character motivations well, then you don't have to do much to keep things moving. It's really simple:
- Don't block investigations, don't try to "hold back" information to slow things down
- People w/info, and clues "throw" themselves at the PCs a lot
A useful game to check out might be Dogs in the Vineyard - since it basically sets up an investigation in every Town, one of the pieces of advice is that there's always someone throwing info at the PCs, just that the info may be biased or edited, or when they're lying you simply tell the players outright, "You're pretty sure this isn't all true" so they know they maybe want to poke at the situation more.