In my opinion, upgrading the Windows OS is never preferred. I agree that building a new server is the best approach to take care of that infrastructure layer. Once your new server is ready, you can install your Application Server platform. If relevant, this is where you can try to upgrade that layer as well. Don't proceed until you're happy with your new OS and AS setup.
Once those are done you can install 14.x following the basic installation documentation from CA. Installing the software does not configure it. It just allows you to perform the next step, which is importing and migrating your IME (Identity Manager Environment).
Exporting your existing IME (from the IM Management console, in zip format), and importing the result into your new environment is just one step, but it is the big one. At this point you should be able to follow the upgrade instructions in the CA documentation. After you imported your 12.x environment into your new 14.x platform, there are additional steps such as updating your roles and settings with the new settings and tasks available in 14.x. Those steps are documented.
Depending on the complexity of your environment, now you copy/merge/migrate your custom BLTH/LAH code, email templates, any manual edits to OOTB IM jsp files, and any other manual modifications made to your original 12.x installation. These steps are tedious and time consuming depending on the complexity of your existing IME.