Just to cut to the chase here - You have 128MB memory permanently on the logic board, and you have a single memory slot that will take a PC100 or PC 133 SO-DIMM, maximum of 512MB, so your maximum memory can be 640MB.
If you want to go to 10.4 Tiger, then you should find out if you have a DVD or DVD combo drive, as some iBooks will have only a CD-Rom drive. Tiger can be found on CDs, but not so easy to find in that form. Normally it will be on DVD.