10.4.11 is the highest possible for that version of OS X. To upgrade further you will need to purchase a Snow Leopard DVD. Check the site below for requirements and purchase info.
The highest version of iTunes you can get for Tiger is 9. It may or may not work with your phone, but its worth a try.
Download the installer here:
Transfer it to your mac through a USB drive, or straight through the mac if it is connected to the internet. Double click it and it will show on the desktop. Install it from there
Don't we need to verify that Snow Leopard will run on the machine?
You may want to post machine info.
blue apple > about this mac > more info button. Click on the hardware line. It has a little triangle in front of the word hardware.
Leave out the serial number.
Machine Name: iMac
Machine Model: PowerMac4,1
CPU Type: PowerPC 750 (33.11)
Number Of CPUs: 1
CPU Speed: 600 MHz
L2 Cache (per CPU): 256 KB
Memory: 768 MB
Bus Speed: 100 MHz
Boot ROM Version: 4.1.9f1