Hi Kitty and All!
It's tough to find a rock that deals only in general matters because, like humans, while stones share universal qualities they also vibrate individually and uniquely. It might also be wise to consider that stones can amplify a negative personality trait as well as a positive one so caution should be used and the selection made very carefully. For divination the type of stone would depend to a certain extent on what type of divination practice is to be conducted and for what purpose.
Generally your Birthstone as described by ancient lore is considered to be the best to have about your body. If that is impracticable or impossible under the circumstances you may want to try this:
Hold a given stone for 5 to 10 minutes, then set it aside. Sit there and listen with your heart. You should 'hear' the movements or vibrations given off, not by the stone
but by your own Self.
Remember that stones are amplifiers for the Universe, not practical power sources in themselves. They are conduits to bring energies from all Creation to you! With that in mind you want to be very careful in analyzing exactly what the nature of the vibrations are doing to/for you; how you think and feel at the moment. It should be PEACEFUL, not powerful. Inner warmth, happiness, and contentment; not the peak pulse of physical or emotional excitement and movable energy.
Hope this helped some! Blessings to you!
One Walker.

We have seen what Power does.
We have seen what Power costs.
One is never equal to the other.