Should I rather go with Drupal or is this possible in WordPress?
It is possible with WordPress. But also with Drupal. Or with Ruby on Rails. Or with Zend. Or with ... whatever programing language you can imagine.
I have no idea where to start. I want to create a widget.
WordPress has a dedicated Widgets API. And WP.SE has a dedicated widgets that offers plenty examples.
with the following features
If you're expecting detailed code, then we're sorry, as this is forbidden according to our FAQ:
Note that we do not handle questions: that require professional hands-on involvement:
overly complex and specific things (known as work for me for free)