From what I can read on Microsoft website, you can only install the "Windows Media Center Pack" from a Windows 8.1 Professional installation. If you have the standard Windows 8.1, you won't be able to install the Media Center Pack. Therefore you'll have to buy Windows 8.1 Professional followed by the Media Center Pack, or just buy "Windows 8.1 Professional with Windows Media Center". In anyway, you cannot buy the pack separately for your current edition of Windows 8.1.
To install Windows 8.1 Pro Pack, you must be running Windows 8.1; to install Windows 8.1 Media Center Pack, you must be running Windows 8.1 Pro.
To be honest, there's no "cheap" way, nor is there a "free" way to get a copy of a Windows OS. The only way to get "free" copies if via MSDN, but even there you have to pay for a licence so it's not really free. What you'll have to do here is to shop online and throught retail stores to find the cheapest price for a copy of Windows 8.1 Professional with Windows Media Center.