iphone 5 info transfer with itunes

I have an old macbook and it will not let me update the software in order to sync my new iphone 5. I think my operating system is too old? Can I use another imac by logging into my itunes account, sync and transfer my information onto my new phone, and then do the same thing on my future imac? Will this still work so I wont lose any information and still be able to use a separate computer?