Changing the primary IP on Linux or Windows VPS's requires editing the network interface settings to use the new IP instead of the old one. On Windows it's done in control panel, network, lan adapter properties, tcp/ip properties. On Linux, it's done by editing the network interface file appropriate for the Linux distribution that you are running. I would say the effort is about the same on both Windows and Linux, so don't think switching to Linux is going to make this any easier and will probably just be harder if you are not familiar with Linux.
In both cases, be aware that you can and most likely will lock yourself out of the VPS when the IP changes to the new one. If you changed the settings correctly, then you can just reconnect (to remote desktop or whatever) using the new IP address and everything is fine, but if something went wrong with the network config, then you will be locked out completely and will need console access in order to fix the network settings. Most VPS providers offer a console access option in the control panel for the VPS, but some do not and you would then be forced to open a ticket with your provider to have them fix it.
Hope that helps!