so:
--adept or mystic adept?
Adept, your already spread too thin, changing just complicates the issue.
--is automatics really the "one gun skill to rule them all"?
If you don't like Automatic then don't use it, you can be plenty effective this game with a pistol, just as long as you build to be effective with a pistol. Automatics has great deal of diversity advantage. But if it doesn't fit with your character image then leave it out.
--if I only took automatics would archery using crossbows be something to consider for easily accessible non forbidden ranged combat options?
Archery is fine, if that what you want to do, it's been buffed in hardtargets, and it can be an effective build, but I wouldn't do both guns and Archery. Archery requires a higher level of commitment in terms of build but can potentially offer a higher level of return in exchange.
--or could thrown weapons work instead of archery?
Thrown is fine, plenty of support for it. Less damage then archery, less commitment.
--keep or ditch Perfect time? nimble fingers? Rapid Draw?
Whatever you feel like works, but there are little weird, I prefer martial arts quick draw. More Skills! You should always always, have some skill enchancement powers, they are the heart of the adept build.
--unarmed combat + adept powers (killing hands elemental strike spiritclaw) or blades+eventually getting a weapon focus for getting past immunity to normal weapons?
Unarmed is very strong build in 5th, a kicking build, get shark mentor spirit, you can push a lot of dice really easily, and you add a lot powers to make it very effective. Blades is fine two, just comes down to what your image of the character, any of those options are good options. You cannot make a good monster hunter without the ability to bypass immunity to normal weapons.
--how valuable would counterspelling and banishing be to this manner of character?
I wouldn't go down that path, as long as someone in the party has CS your fine, Banishing is easier to handle just by being able to take out spirits.
--how valuable would the physical and/or mana bind and net spells be to this manner of character?
Lots of solid spells available, binds nets would not be my first choice, but it could work.
--would either or both of the previous points be worth being a mystic adept?
No. You can get a spell as normal adept, and it keeps the build more focused.
--for the investigation angle, is analytical mind worth the karma? is analytics worth the power points?
I'd run high perception and enhanced sense, particularly smell, ascencing is double edge sword, and it would be something I'd build into.
--what skills besides perception would help with investigation type stuff?
Animal Handling, wilderness survival, various lore skills, ascencing