How much stone do I need for a 9 x 9 area?

1 inch seems a little thin. You may want to use 2-3 deep. I would use gravel 4 or 57 (some people call river rock). I would say 3/4 to 1 ton would be a good amount. For mulch I would use either a recycled rubber mulch, or playrite. it is a mulch that is certified to reduce injuries by up to 80%. (If spread 6" thick). I'm sure there are different brands. That is just the brand we carry at my place of employment.

Assuming you are talking about 9 feet by 9 feet, you will need approximately one quarter cubic yard.

Having said that, 1" thick is not very much and it will not last very long under the swing set. I suggest you get one cubic yard which will give you a 4" thickness. Then you will have enough material to last a lot longer.

Also, you will be able to maintain the gravel bed by raking it back into place from time to time.

I would reccomend some kind of river rock if you are using it for a swing set area, and you would probably need 800-1000 lbs. It sounds like a lot, but its not that much when you start spreading it over 9 feet