You'll need to upgrade to at least OS X 10.6.6 or later to access the App store. You already have an Intel processor and probably already have the 1GB of memory required for OS X 10.6. Call the online Apple store, which in the US is at 800-MY-APPLE to order OS X 10.6 Snow Leopard. Install, do Software Updates, and you'll be at OS X 10.6.8.
Your Mac Pro needs to be a 2008 model or newer to upgrade to OS X 10.8 Mountain Lion, and while the minimum memory is 2GB, 4GB is recommended. Once at OS X 10.6.8, and assuming your system can run it, you can buy and download OS X 10.8 from the App store.
If you can't run OS X 10.8, you can still buy OS X 10.7 Lion by calling the online Apple store. They'll send you a code to download it from the App store. OS X 10.7 has the same memory requirements and recommended memory at OS X 10.8.
One other thing to be aware of .... in both Lion and Mountain Lion, Apple dropped emulated PowerPC support, so if you currently run any programs with PowerPC code, they will no longer work. People upgrading with Office 2004 got surprised when it would no longer work.