/ - root should have enough space for the entire OS and additional software. In my experience, it's better to assign at least 100 GB, for applications, games, etc.
/boot - boot partition should have at least 250 MB.
/swap - This depends on your installed RAM or memory. If you have 4GB of RAM or less, assign 2GB or more.
Kubuntu is a flavor of Ubuntu that uses KDE as Desktop Manager like Gnome or Unity for Ubuntu. There are others, like Xubuntu for lower-cpu computers, Edubuntu for schools and others.
Check-out their website: www.kubuntu.org