What are good strategies for deciding which expeditions to start in Lost Cities?
1) You want to wait, but you can't wait all that long.  Sitting there with half your hand made up of cards that you don't want to play is normally a huge problem in Lost Cities, and you risk giving up a huge amount of tempo to your opponent, in the very small hope of drawing one specific card.  Sometimes you just have to quit hoping and start playing - after all, your opponent may have those investment cards in HIS hand!  (Of course, holding out can result in the dream scenario - your opponent laying down multiple investment cards for a colour in which you hold a balance of points...)

2) With multiple investment cards?  15 sounds a safe-ish bet.  But let's not forget that you can embark on expeditions without investment.  I'm perfectly happy to start off expeditions with barely any cards sometimes - just because putting pressure on and psyching out your opponent can easily be worth the potential loss of 10+ points.

3) As above.  I certainly would, but I almost certainly wouldn't risk multiplying my losses by 3 or 4 by playing investment cards first!

4) Possibly the most difficult scenario - you don't want to discard high cards and you don't want to play high cards, so what do you do?  It can be quite good to bait your opponent by discarding medium-value cards, while holding the higher values so when they snap your discard up, you know they're on a hiding to nothing.  But I agree, it's a hard situation to deal with comfortably.  (Then again, it's difficult for me to feel much sympathy for someone whose "problem" is being dealt a hand of strong cards!  Just play out an 8-9-10 for +7 points, and see what you draw in the meantime: a few investment cards would obviously have been nice to have, but it's not like you've really lost anything, is it?)