Why I can't recommend Arch or Gentoo

[Kyle]

Arch and Gentoo are essentially designed for OEM's and DIY folks. Of
course they're not going to have a desktop coming up on the live image.
That's not the problem they are designed to address. Arch and Gentoo
are designed to start from nothing and give you exactly what you want.
If that's not your thing, then either don't use it or set it up for
someone who wants a customized desktop.

For Arch that comes up with a desktop, try Manjaro, or if you need it
to come right up talking, Sonar would be your thing. These are not pure
Arch distros, but they instead copy the Arch repositories and make some
changes downstream at the distro level, and they come up with graphical
desktops based on the iso you download.

For a desktop Gentoo, give Sabayon a try. It's somewhat of a Gentoo
fork, but it's actually more of an overlay. I believe it has GNOME and
MATE versions, and it even has its own binary package manager, though
it also works with Portage. Just a heads-up though, I believe they
still recommend using the binary package manager first, and Portage
only if you can't find a binary package. I think they do some
downstream distro-level things as well. Hope this helps.
Sent from my silver lining