I use KDE as my desktop. KDE is installable on any distro, although you probably want a distro with a newer version of it like Fedora or Opensuse. On KDE, these two shortcuts do what you would expect them to do.

Win + V opens up a clipboard manager by default:

I actually like this clipboard manager better than the Windows default clipboard manager, because it lets me search, edit, or star items so they can be found quickly from the "starred only tab". The amount of items kept is also configurable, and it keeps way more items than the Windows clipboard manager.

Windows + Shift + S opens Spectacle (KDE's screenshot utility) by default. It has some basic editing features, but one feature about it I like is there is an option to upload the screenshot directly to imgur for easy sharing.

For RDP, I recommend using Remmina to connect to machines via RDP. It supports shared clipboard, but also shared filesystem and some other nice stuff. You can save connections and their options to easily connect again later.

Remmina is a mature program that is available in the repositories of most Linux distros.