Without knowing which build system you're using, I can only really say general things. It's difficult to build a really competitive 'completely mundane' character, but it's damn fun to try. If you plan on keeping the build mundane forever (i.e. after he's survived a while) then it's even tougher cause you have to really think about future karma spending in CharGen cause you won't have the the luxury of fixing all your problems by just adding some ware (e.g. "just slap some muscle toner 3 on him") or initiating. With that useless monologue out of the way, I guess it's really a question of what kind of investigator you want to be, so I may not be thinking what you're thinking here.
As far as main attributes I would think Intuition & Willpower. Intuition for the skills perception, shadowing, possibly tracking, and possibly assensing (see below). Willpower because, let's face it, the second that 'occult' thing you've been 'investigating' decides to make your soul a snack that's your main method of defense as a mundane. If you're using a BP system, Logic might be a investment you have to make to get all the knowledge skills a good occult investigator would have (e.g. magical threats, conspiracy theories, parazoology, etc...).
If it doesn't break your concept, consider taking the astral sight quality (SM 24), this would enable your character to actually see if there are spirits in the area, otherwise your character could only just 'have a bad feeling' about a haunted house or something (reference: Every episode Ghost Hunters and Scooby Doo). Astral sight quality gives you access to both the assensing and astral combat skills. Other positive qualities to look into: magic resistance, analytical mind, perceptive, common sense, fame ("the famous ghost hunter"), & day job. Bad qualities that might be fun: cursed (if you take astral sight), bad luck, delusion, distinctive style ("the tin foil hat wards off wendigos"), phobia, paranoia, hallucinations, and will to die.
Useful skills: perception, stealth skill group, tracking, assensing, astral combat, data search
If you do go the astral sight route look into getting a weapon focus. Get vision enhancers and audio enhancers of some sort with at least their respective enhancement mods at 3. If you're using a gun, get ammo that can actually hurt magical things (e.g. ex-ex, stick-n-shock, silver bullets). Decent commlink with a browse program.
Anyhow that's just some thoughts, so hope you find a good build. And if you're doing a BP build and you haven't already read emsquared's guide (
http://forums.shadowruntabletop.com/index.php?topic=10206.0) do, it'll help you squeeze out some extra points.