I recommend Ubuntu, tried a few times when I needed a full system asap
I'm not familiar with kubuntu, so Imho the "normal" ubuntu live would be ok for you. In case your hd isn't fried, it's safe to mount the partitions, OR even better: if you have an USB stick that has a few gigs space, you can try to format a partition from it as ext3, so you can put stuff there (yeah, I know USB sticks are not for a lot read/write, but they can be serve as a last resort anyway).
So, here's what you can do with the power of a live CD:
1.: launch up the system from the CD
2.: in case drives aren't fried: mount them, and you can use them as you wish

If they are ntfs drives, you should iirc install the ntfs-3g package: in a console, type in:
sudo apt-get update
sudo apt-get install ntfs-3g
After that, you can mount your old drives (there are a lot readme for manual mounts, it isn't hard, in fact, one of the most easiest tasks).
3.: in case there's a HW problem, I recommend you to format an USB stick for ext3, and pack your stuff there. Why ext3? Because afaik that's the default for *buntu, and ext has the ability give files permissions eg. "run" (fat32 or nzfs can't do that).
4.: if you'd like to play 3D games, you can even install the proper ati or nvidia drivers in live mode! The trick is: once you've installed it from the menu (there's a menu option for that), the system will ask you to restart the pc. But you don't restart the whole system, we're on linux after all

. Restart only the graphical interface (X server) with CTRL+ALT+BACKSPACE, and voila! you have 3D accelaration too!
Ubuntu uses apt, so any apt related manual will be ok for you for installing new programs (they come in packages, and apt will handle all the stuff for ya). One thing you should be aware of: the system uses your "RAM" as a hard drive, it'll dowload all stuff into there (thy can be listed however just like they were really in your file system). Once it tells you it's full, you should move the downloaded stuff to a permanent place (either the HD, or an USB stick).