I need to upgrade my operating system. What should I do first?

You didn't say where you need to upgrade to, or for what ... so here's the path to get you current.

First, install OS X 10.6. This is available from the online Apple store, which in the US is at 800-MY-APPLE or online here. See this article on installation considerations. Ensure you have have a solid,bootable, backup before you start. Plan to erase and install then transfer files from your backup.

After you install OS X 10.6 and do Software Updates, you'll be at OS X 10.6.8. From here you can upgrade to either OS X 10.7 Lion or, assuming your iMac is a mid-2007 or newer model, to the current OS X 10.8 Mountain Lion. Unless you have a reason to upgrade to Lion, you should probably go straight to Mountain Lion. Note, both Lion and Mountain Lion have a minimum memory requirement of 2GB, which you have, however, 4GB is recommended.

You can order OS X 10.7 Lion from the online Apple store, which in the US is at 800-MY-APPLE. You can download OS X 10.8 Mountain Lion directly from the App store (you'll have the access program on your OS X 10.6.8 system). You can go directly from OS X 10.6 to OS X 10.8, you do not need to install OS X 10.7 as an intermediate step.

If you have any PowerPC programs, they will no longer work under OS X 10.7 Lion or OS X 10.8 Mountain Lion. Some were surprised when Microsoft Office 2004 no longer worked after the conversion.

Why do you need to upgrade your OS? What is wrong with the version you are now using?

Yes it is very confusing, but that's Apple for you.

you will need to contact Apple by phone and order the Snow Leopard Upgrade DVD disc which will be mailed/shipped to you. Once you have that DVD you install it over the top of your current version of OS X and then ryun Software Updates several times to get all the updates available for both the newer OS and the software on your system.

Until you call, order and wait for delivery there isn't much else you can do.

you will need to contact Apple by phone and order the Snow Leopard Upgrade DVD disc which will be mailed/shipped to you.

Shootist 007,

That is Incorrect information, all the OP needs to do is click on Snow Leopard upgrade page then purchase Snow Leopard. When the DVD arrives follow the enclosed instructions and then click on 10.6.8 Update Combo to download and install. Once that has been done then simply run Software Update and install all the recommended update. Extremely easy and in most cases very little drama involved.

However to answer the OP's first question of what they should do first, the answer is simple. Back up everything, if he has the ability he should run Time Machine to backup and if not then create a bootable clone using either SuperDuper or Carbon Copy Cloner.

It is Not incorrect info. Unless you are saying you CAN NOT order it over the phone.

Please leave me alone. I post what I know to be correct information. If there are other ways to now get Snow Leopard, there wasn't originally after Lion and then Mt Lion came out, I did not know about it.

So instead of trying to belittle me just post what you know to be the alternative ways of getting it.

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We now have an iPad 2, an iPhone 4s, and an iPod Touch in our household. All of which are not recognizable by the current version of iTunes that I am running (which is the most current version I can run of OS X 10.4).

Will simply upgrading to 10.6 be enough?

Yes, upgrading to OS X 10.6.8 will be enough, because iTunes 10.7 is what you need to sync everything up, and it requires OS X 10.6.8. You don't need to go to Lion or Mountain Lion at this point in time. Just OS X 10.6.8 and iTunes 10.7.

I would say that's a seperate question best asked in the relevant forum - https://discussions.apple.com/community/ipod/ipod_touch