You can copy your music off your iPod onto your Mac with [guide]Senuti[/guide], but once your music is on your Mac, the iPod should "just work" with the Mac as it can read PC formatted iPod's natively.
The first time you connect your iPod to your new mac, iTunes should ask you if you'd like to transfer all the files from your iPod into iTunes. If you have any iTunes purchased content (DRM), you'll have to add that computer as an authorized computer (you're allowed up to 5 I think).
Like mentioned, you won't have to format your iPod into Mac format if you don't want to - Mac will recognize a Windows formatted iPod, but Windows won't recognize a Mac formatted one...
If this doesn't work for you, try using the official method, or just transfer using third party software as mentioned above.
You cannot transfer music from iPod to computer without an application such as Senuti, which should work fine if you have a classic or nano (it might work with a Touch, although it didn't when I tried, but I'm guessing they've brought out a workaround by now). Or if you have a classic, then enable it as a hard drive (doesn't work with the Touch).
However by far the easiest way is to turn on file sharing in system preferences, and transfer the music across over the network, or do you have a external hard drive?