Yes it is easier to install and upgrade them on Linux (at least I find it easier) - its usually a simple apt-get install command, or similar depending on your Linux distribution. But if no-one in your institution (you) has Linux expertise, but you do on Windows then, for all its benefits, moving to Linux may not be the best solution in your particular case
That said, if you were to install Linux now and then install the apache, php and mysql requirements they would probably be the latest anyway (although I dont think many distros have PHP7 in their default repositories yet), so the issue becomes installing/using Linux rather than upgrading the server requirements, but subsequent upgrades would be straightforward.
