I would like to upgrade my 13" Macbook running 10.4.6 to a more current OS.

Why is what so complicated?

What is the model of your MacBook?

You can find it in System Profiler. You can access that by going to About this Mac in the Apple menu and clicking More Info...

When the profile appears, click on Hardware.

You should see a model name and a model identifier.

If those labels don't appear, look for something like macbook1,1.

Once you find the model number, you can look here to see when it was manufactured:

http://support.apple.com/kb/HT1635

The age can determine how far you can upgrade.