Become a MacRumors Supporter for $50/year with no ads, ability to filter front page stories, and private forums.
How would I move my iTunes music file and photos along with Firefox and all it's bookmarks to another Mac from my current Mac?

There's a thing called 'migration assistant' that should be on your new computer that will help you do this easily. Never tried it myself, so maybe give it a go and report back your experience?

To find it, just type 'migration assistant' into the spotlight search box.
 
alternatively, you could hook your old mac up to your new mac via firewire. turn on the old mac while holding "T" and it'll boot up in the firewire disk mode. you can drag all your files from the music and pictures folder over, and everything should copy just fine. also, you can export your firefox bookmarks, and import that file from your new computer.
 
How would I move my iTunes music file and photos along with Firefox and all it's bookmarks to another Mac from my current Mac?

Or, failing those two, you can try:
Burning the relevant folders to CD or DVD
Using a USB pen drive
Connecting the two computers via ethernet cable
Connecting the two by creating a wireless network on one
Etc.
 
Register on MacRumors! This sidebar will go away, and you'll see fewer ads.