I used to install the Outlook app, because it was the only way to get shared hotmail calendars to show up in the stock Google Calendars app. Then one day a couple months ago I tried uninstalling Outlook and just using the built in email app and my calendars still worked! So I've kept using that because it works better than the Outlook app, looks better, and matches the GMail app.
Don't use the Windows Mail or whatever for your mail type, use Exchange. There's instructions how to setup the servers, but it works way better than fighting with that built in Windows Mail server type.