You don't say what machine you are running. Before you bought anything, you first should have made sure your Mac is compatible.
Minimum specs for Snow Leopard. Mac OS X v10.6 Snow Leopard -Read the Technical Specifications
Note. You can no longer buy Snow Leopard from an Apple retail store, only as follows.
If you are in North America ... you must call them (1-800-MY-APPLE). last I read It is $29 plus tax for family pack and $19 plus tax for the individual use version.
In Europe or otherwise … call your National Apple Helpline. Find it at … http://support.apple.com/kb/HE57
Once you have bought and upgraded you will need to apply the Combo updater for Snow Leopard. Mac OS X 10.6.8 Update Combo v1.1
You can get iTunes 10.7 from Snow Leopard. You do not need a higher OS.
All the same, upgrading to Lion / Mountain Lion.
For Lion, the minimum specs are …OS X Lion - Technical Specifications
Download code to be bought from Apple.
For Mountain Lion the minimum specs … technical specifications.
You can go directly from Snow Leopard to Mountain Lion via the App Store, providing you meet the specs.
Not necessarily. You need a mid 2007 or later version, Intel core 2 Duo and at least 2GB of memory. (4GB would be better.) If you have that you can upgrade as per stage one of my first post.
Sadly the computer world moves rather faster than our bank balances increase (at least, I find it so). All the same, for basic personal needs your machine could still be good for several more years ... it's all a question of what new facilities you want.