howmuch sp do you need to complete the Saggitarius's Quest:

750k (750,000 sP) after purchasing the items.

Does that have to be on hand? Or you just have to have 750k in your account (on hand + shop til + vault)?

Just in your account, but I always suggest having 850k, because after you buy the items, if you have less than 750k, you can't complete the quest.