You can use Fedora, Debian, Whonix, or Windows in "seamless" mode with minimal effort. It has a composable networking architecture (e.g. easy to make all a VM's traffic go through Tor, whose traffic in turn goes over a VPN). Disposable VMs are a native feature. Template VMs reduce duplication of /; Application VMs use a template VM with CoW / and their own persistent /home.
Qubes uses Fedora 20 for Dom0, so you get all the same graphics support as Fedora gives you.
Debian is what I'm most familiar with, so that's my new place to go. Still quite big with a relatively basic install, but not as big as Ubuntu or Linux Mint.
Really lightweight stuff is Damn Small Linux (old) or Puppy Linux (never tried it), but I'm not sure how usable that is for day-to-day tasks.