Download 8.04 (LTS), burn it to CD, boot from it and install. 6.06 is no longer supported by Ubunutu, so no security upgrades.
I advise that you get the alternate install CD , the 'normal' one requires more memory (although according to the requirements it should install). When installing, only create a swap partition of 512MB and a root partition (/). With the amount of harddisk space that you have, you will loose too much by further partitioning (one of the partitions will still have space while the other one is full).
Your hardware will be OK (it just matches the minimum requirements), but the performance will be low. Have a look at more minimalistic distros like DSL, Puppy and others.
Last edited by Wim Sturkenboom; 10-18-2009 at 08:28 AM.