I had no idea that they exchanged the newest for stability/etc. I installed it last night, and it's the first time I've ever used KDE 3 ...

But tinycore is Slackware-based, now, in its recent incarnation, isn't it?

As the OP asked for a live distribution: I like SLAX a lot. It's an unofficial port that allows to create your own Slackware-based distro in the simplest manner I have seen so far, and it fits on a mini-CD or USB stick.

I recently put in on a USB stick with two partitions. One for the system, and a LUKS encrypted one for data. On that second partition I carry all my access and account data with me, when I am travelling. I prepared the stick and the partitioning on my Slackware desktop, then put SLAX onto it, and it worked right away. And if you like it, you can install it to your hard disk, and even make an "official" Slackware install off it, later, using the standard package management tools.

BTW, while in the past there have been lots of derivatives of other distros appeared on the market, but in the recent past, Slackware seems to become a preferred basis for deriving customized distros. Fluxflux is just another popular example.

gargamel


EDIT:

As to Arch, I found these:
I am a complete GNU/Linux beginner. Should I use Arch?
Is Arch Linux a stable distro. Will I get frequent breakage?
Arch needs a stable branch

Arch has a very good reputation, maybe the best among all "source-based" distros. But number 2 is why I prefer Slackware. The team just ensures stability, I concentrate on what I want to do with the system, not on the system as such.

I have used both Slackware and Arch.
As others have said, Slackware aims for stability and is conservative. Arch is bleeding edge. As a result, things are more likely to break in Arch; and you will need to read up on how to fix them. In Slackware, nothing ever seems to break.

Arch's Pacman works well, and manages dependencies.

Slackware uses manual dependency management. This is preferable to people who appreciate the way Slackware does things. It is a choice you make. This is not as difficult as it may sound, thanks to the excellent slackbuilds provided by everyone at http://slackbuilds.org/.

Both distros give you total control over what gets installed on the system. Both distros have excellent documentation. Try them both. You will learn a lot.