Simple question about updating my Macbook.

I just bought an Iphone 5 and try to plug it in to the computer, computer tells me the iphone requires itunes 10.7. I think this is a misscript and it actually means that the software is out of date on the computer. I did some research on here and have come up with i need 10.6.8 on my computer. I am not sure if i need a new computer or if this computer is even capable of downloading the newer os. I will list what my computer is, and if someone would tell me what is the best route, or if i need a newer mac...then it would be greatly appreciated. Thanks in advance.

Hardware Overview:

Model Name: MacBook
Model Identifier: MacBook3,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.2 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 4 MB
Memory: 2 GB
Bus Speed: 800 MHz
Boot ROM Version: MB31.008E.B02
SMC Version (system): 1.24f3
Hardware UUID: 537DD8CC-51C2-5234-94AF-E78CA658DACA

Intell said:

Snow Leopard will run fine on that machine. You can even run Lion on it. But I suggest upgrading the ram to 4GB if you want to run Lion.

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So all i need to do is purchase snow leopard? The guy at apple support told me this machine was currently running it. I dont want to change the computer around at all..

Intell said:

Click on the Apple menu in the top left of your screen and click on About this Mac. In the window that opens you should see it say either 10.5.8 or 10.6.8. What does it say?

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Sorry i forgot to mention that. 10.5.8...

Intell said:

You have Leopard on that machine. You'll have to get Snow Leopard for that machine.

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Do i need this? and do i need to store everything on an external storage device to not lose music or photos??

http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard

In other words i upgrade to this and then my itunes will work with the free update to 6.8? Also they no longer have a downloadable version of this? From what i understand...