Need help with interactive calendar

I need ideas about incorporating an interactive calendar into my website. A calendar that registered users of the website can enter their own events, add to their personal mobile/desktop calendar, and input and sort by county of the event. Basically, the functionality of Google calendar, but the ability for members to add their own information. I’m wondering if this can be made exclusively for my website. I just want to remove myself from managing the calendar if you know what I mean. I’m open to using a third party calendar, but have no idea which one is the best. Also, I’m not excited about the monthly fee that would probably be associated with it, but if it is the best way to go, then, it is what it is. Thanks!