how can i restore info from my hard drive to my new mac

I have an "old" black macbook, that I have backed up on an external hard drive using time machine. I recently got a new (aluminum) macbook and i want to transfer my data from my hard drive to my new computer (itunes library, photos, etc...). I do NOT have ilife or iwork on my new computer, but i have it on my old macbook which (in theory) should be backed up on my external HD. Is it possible to transfer applications like that to my new computer if I "disable" it from my old computer? I also just got a new iphone 5 and would like to be able to sync it to my new computer but my itunes library is empty (until i take stuff from my hard drive and put it on my new computer). Obviously my old macbook will not support the software needed to hook up my new iphone to itunes, but my new computer will. So I beg the answer to my question...how do i get my stuff from one computer to the new one and can i transfer applications such at iphoto, pages, (ilife, iwork)...legally by disabling from my old computer?????

PLEASE HELP!