You are farther behind than you suspect. Since OS X Leopard 10.5 - 10.5.8 there have been;
OS X Snow Leopard 10.6 - 10.6.8
OS X Lion 10.7 - 10.7.5
OS X Mt Lion 10.8 - 10.8.5
OS X Mavericks 10.9 - 10.9.3 and counting
If you choose to upgrade from Leopard to Snow Leopard the retail disk that you by from Apple for $20 will bring your Mac to 10.6.3. You will want to update to 10.6.8 using the update combo below. This will give you the final public release version of the Mac App Store (MAS) with which you can buy many apps for your Mac, some of which are free. Unfortunately because you will still be running a legacy version of OS X, many MAS apps will not run on your Mac, they require a newer version of OS X. The version of Pages now sold in the MAS, for example, will only run on OS X Mavericks.
OS X Snow Leopard 10.6.8 v1.1 update combo
http://support.apple.com/kb/DL1399
OS X Upgrades -
A Mac that can run OS X 10.6 Snow Leopard can usually run OS X 10.7 Lion. And a Mac that can run OS X 10.8 Mt Lion can also run OS X 10.9 Mavericks. Lion, Mt Lion and Mavericks can all be installed over OS X Snow Leopard 10.6.8, so you may upgrade from Snow Leopard directly to any of the other three. Both Lion and Mt Lion are paid upgrades, while Mavericks is a free upgrade. You may also upgrade directly to Mavericks from either Lion or Mt Lion.
System requirements for OS X Snow Leopard & OS X Lion
http://support.apple.com/kb/ht4949
System requirements for OS X Mountain Lion
http://support.apple.com/kb/HT5444
System requirements for OS X Mavericks
http://support.apple.com/kb/ht5842