I would like to have a mini calendar web-part on the page that gets data from the calendar list.
Something like this picture
Had the same wish for my SharePoint environment, but I didn't find anything I liked.
So I took the default stuff and made it "ok".
Two days ago, I posted the english version how I did that.
Maybe it will fit for your requirement, too.
You can try this web part - MiniCalendar Web Part
We had a similar requirement and discovered the following useful example for a custom display template using fullcalendar.js:
I personally found this quicker and easier to deploy than a custom app plus it integrates nicely with search for cross site collection queries.
Only issue I currently have is the 50 item limit for search results (raised a question here looking for a solution: https://sharepoint.stackexchange.com/questions/128879/sharepoint-cswp-50-item-limithttps://sharepoint.stackexchange.com/questions/128879/sharepoint-cswp-50-item-limit)