Support for Windows Vista (and XP) was dropped when Apple released iTunes 12.2 last year. The latest (and almost certainly last) version to support Vista is 12.1.3.6 - this is an out-of-sequence release from September 2015 that adds support for iOS 9 devices but lacks Apple Music and other features added in iTunes 12.2 and 12.3. Links to the installers:
The last of these is actually (like all "64-bit" editions of iTunes prior to 12.1.2) the 32-bit application with a 64-bit installer - this should be used if you get a warning message about video card incompatibility and may also address issues with poor audio playback, integration with 3rd party software, and general stability of iTunes.
Note also that no version of iTunes since 11.1.5 has been fully compatible with Vista; all subsequent versions consistently generate Data Execution Prevention errors on exit. Since Vista is just a little more than a year away from complete withdrawal of support by Microsoft, you really should be thinking about replacing your computer or updating it to a more recent edition of Windows. If you want to make use of Apple Music you will have to upgrade to Windows 7 or later.