My game, that I plan, it's like the movie Cabin in the Woods. It's much like a slasher movie, with teen agers at a summer camp, doing naughty things. But, they're hunted by killers, and they're part of a big government experament.
If you want to emulate the genre, among the free options, there's nothing better than FATE.
The reason is the mechanic called Aspects. Characters get FATE points for doing genre-appropriate things that might get them in trouble. Stuff like checking on the suspicious noise in the basement without calling anyone for back-up is a prime example here, often used to describe Aspects
So, just make them take an Aspect describing the role their character would play in a slasher movie. The Nerd, The Girl in the couple, The Boy in the couple, The Lone Girl, whatever. Then let the genre guide you
Why do people even want those FATE points? Well, in return, you get to use those points later to improve your odds of success with, say, your Athletics skill while you're being chased. Or you get to declare something genre-appropriate, like the existence of a stone near the place the killer is struggling with your character on the ground. So basically, players are bribed into doing the genre-appropriate stuff
(Well, or if the above doesn't sound interesting for some reason, point me what's wrong with it, and I could probably suggest something else. For that matter, I could probably hack a system for you. It's usually simple with a bit of practice, barring some really unusual requirements).
I think much of my game, it can be free form. But, for when there's fighting, and trying for escaping, I think I'm needing rules. Also, I may be think I need rules, for characters noticing clues, or solving the puzzles, I need rules, too.
And you just described how many "system" games go anyway. There's a misconception that you roll for everything. In practice, most things are just the way you declare them to be. There's even an explicit rule in some that only high-stress or important actions are worth rolling. Everything else succeeds automatically, or fails automatically, as the player or GM declared it. I mean, if it's not important, why stop and pay it special attention?
I never play a role playing game, with rules, before. All of this, it's very new, to me.
Remember that you can ask if you've got questions. I doubt there would be a shortage of answers