Bought music from iTunes can be copied to the PC by right clicking on your Ipod in the device list and choosing "transfer purchases".
For all other media you'll have to use 3rd party software, like Touchcopy for example.
If you haven't synced to your new computer, remember that iTunes will erase the content during the first sync.
To save your data and settings do this:
Disable autosync in iTunes, connect your iPod to your new computer and right click on it in the device list and choose backup. iTunes will backup your iPod without syncing.
Transfer your purchases the same way, choosing "transfer purchases" this time.
When you connect your iPod for the first time, all media content will be erased. But you can restore your settings and app data from your manual backup afterwards.
Don't forget to set up at least one contact and event on your new computer to be able to merge calendars and contacts when you sync the iPod for the first time.
Music is one way only, from the computer to your device, unless you bought the songs in itunes and transferred your purchases.
There is 3rd party software out there, but not supported by Apple, see this thread:http://discussions.apple.com/thread.jspa?threadID=2013615&tstart=0
About backups and what's saved: iTunes: About iOS backups
How to back up and restore:http://support.apple.com/kb/HT1414
How to download apps for free again:http://support.apple.com/kb/HT2519
Saving other data is also described here. How to back up your data and set up as a new device
