upgrade osx from tiger 10.4.11

With those specs you can start with upgrading to Snow Leopard.

Whilst Apple have withdrawn Snow Leopard from their stores, you can still get it from Apple by calling 1-800-MY-APPLE (if you are in the USA) and they will supply the SL DVD for $20 for a single user, or $30 for a family pack that covers up to 5 Macs. You can also purchase the code to use to download Lion from the same number (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:

http://www.apple.com/osx/specs/

If you are outside the US call your national Apple Helpline:

http://support.apple.com/kb/HE57

If you're in the UK, use this number: 0871 508 4400

When you have installed it, run Software Update to download and install the latest updates for Snow Leopard.

To use iCloud you have to upgrade all the way to Mountain Lion:

http://support.apple.com/kb/HT4759

You will have to request an 10.5 disk from Apple, then a 10.6. Then, buy the 10.7 update from the Mac App Store.

Or, you might be able to just update to 10.6 without needing the 10.5 disk.

Am I correct in trying to get my new Macbook and Airport Network all in sync OSx wise?

That can only help. You shouldn't have problems in that regard after you have finished updating.