It really depends on what you want your story to focus on. Obviously the mystery but I mean where you want your main character to be. Emotional? I'd make it start with the sister missing so you can see the turmoil of realizing her sister is missing and then get to the finding part. Or if you want her more motivated and calculated I'd make it that she's been missing for a few months or so.
Well the sister's death is virtually your whole story. But some ideas could be murder, accidental death, suicide, suicide that looks like murder, murder that looks like suicide (really any of those combined). Fake death and she's really a lounge singer in the Virgin Islands. Or something. :P