You need to buy Snow Leopard first because the only way to get Mountain Lion is through the Mac App Store. For advice about how to get Snow Leopard (10.6.x) check the links to the right in the "More Like This" section of this page.
Also make sure your Mac meets the minimum system requirements before buying the upgrades.
You can only upgrade your Mac to Snow Leopard if it has an Intel and not a PowerPC CPU. Tiger ran on both...
Then Mt. Lion has minimum system requirements to allow the further upgrade.
BE AWARE: Mountain Lion no longer contains Rosetta, the transparent emulation software that allowed PowerPC applications to run on Intel Macs. Snow Leopard, optionally, does, so you may not even be aware that you are still using these apps.
If you do an About This Mac and check Software for PowerPC, let us know which ones, if any, you have that you need access to in Mt. Lion.
It would be best to be proactive about this issue BEFORE you upgrade to Mt. Lion.