You have to understand the difference between an Update and an Upgrade.
An Update is a free change within an existing Operating System. Such as the .8 added to 10.5.
An Upgrade is a complete new Operating System that must be purchased. Such as 10.5 Leopard to 10.6 Snow Leopard.
10.5 code was written to be able to run on both Power PC and Intel. 10.6 has completely rewritten code and only runs on Intel Macs.
To see which model you have go to the Apple in the upper left corner and select About This Mac, then click on More Info. When System Profiler comes up check the Model Identifier and post it back here.
The Early 2006 model 1,1 Core Duo can only run a maximum of 10.6 Snow Leopard.
The models Late 2006 Core 2 Duos 2,1 through Early 2008 4,1 can only run a maximum of 10.7 Lion.
The Late 2008 model 5,1 Aluminum Unibody through the Mid 2010 White Unibody model 7,1 can run 10.8 Mountain Lion.
You have to upgrade to 10.6.8 to be able to download iTunes 10.7. The Snow Leopard 10.6 DVD should still be available at this time from Apple for $20. You will have to call Apple Customer Care 1-800-692-7753 or 1-800-676-2775 to purchase it. It may still be in the Legacy Products list. The App Store which is required to download 10.7 Lion or 10.8 Mountain Lion is part of the 10.6.6 update.
If you wait to long and they no longer have any in stock you will have to buy it from eBay or Apple resellers that still have stock. But you will have to pay a premium since the DVDs are no longer being made. Snow Leopard DVDs are already up to $100 on Amazon.