Personality makes for a better experience of that character. The most interesting background in the world won't matter if they're as dull as a butter knife.
But the backstory for a character matters a great deal, even if you're the only one who's ever going to see it. Spend some time writing out a character bio for each of them, and if you're really up for it a basic timeline of important events in their life. It'll help you get a more solid idea of who they are in your head, and more importantly give you some sense of their motives and desires. A character without any motivations is a plot device, not a character. Again, their specific motivations don't need to be related to the game, or why they're in the chalet.
A guy who has a family, who is motivated to give his daughter a better life than his, is going to be extremely concerned with getting home to his family. Compare that with a second character who's business just went under, and blames the first character for it and who's primary goal in life is to get even. The second guy might try and frame the family figure for the murder, or kill him in addition to the murder in the hopes of getting away with it. Is the daughter at the chalet? Will the father be willing to commit morally heinous acts to protect her, or avenge her if she's hurt?
Is the third character a former detective, who was forced to retire after they failed to solve a case? Has that failure haunted them? Could they see this as a way to redeem themselves, and to what extent will they go to do so? Does saving people from the murderer matter more to them than catching the killer?
Whenever I write a story, I tend to develop my characters like this first. Then when I stick them in a situation (the chalet) and throw a problem their way (the murder), I have some idea of what might happen next for each of them. Your players need not ever encounter or find out about the vast majority of your character's lives if it never becomes relevant to their experience of the game. But it can really help you in making fleshed out people for your story - more than just walking plot devices.
If you're looking for inspiration to get started, there's a ton of random character generators available online. Pick one and see what it comes up with. Do any catch your eye as being interesting, or something you can morph into a person in your story? Use these random characters (or even people you know) as a blueprint for your characters that you can mould into something that works. But don't just copy-paste them from the generator into your game - there's no guarantee they'll fit with what you want.