If I'm right, when you bought your new phone the Mac says you need an updated version of iTunes, (which requires and updated OS)?
I Believe what you need to do is first purchase Snow Leopard because the later OS need the Mac App store to work.
Before you proceed you need to do three things;
1. Back up your Mac, using preferably a clone. SuperDuper, Carbon Copy Cloner or just using Disk Utility from the Mac install DVD will work. If you want to take this step which is well advised post back and we'll take you through it. You will need a USB/Firewire External hard drive to do this with that needs to be at least as big as your internal drive. CCC and SD are easier but DU is the option that works more simply without issue on the later OS versions.
2. Make sure that your Mac meets the Specs for Snow Leopard and Lion, Mountain Lion and Mavericks should you choose to go further. If you opt for Mavericks instead of Mountain Lion or Lion, make a note of what's said here.
3. Make sure that any existing software/hardware you have will work with the new OS. I do not mean just third party software. There is some Apple software that works only older OS.
