In addition to Mint and AntiX there is also Slackware (I use xfce rather than KDE) but adding software outside the (large) base install is not an 'apt-get thing' process.
Salix Linux, based on Slackware, does have package repositories with a reasonable selection of applications. Salix is based on the stable Slackware 15.0 so has nicely aged packages.
Void Linux also has an xfce4 based live i686 iso you can look at and decide to install from.