Yes, you can sync Music, Apps, Books, etc. from your iTunes library on your computer. A couple of questions, and then we can go from there:
What type of Apple Computer do you have?
Do you currently have a music library in iTunes on the computer?
Do you have the most current version of iTunes loaded on the computer?
If you can let me know the answers to those questions I can provide you with a couple of links that would be helpful....
Well, I think there may be a problem....you are running Tiger, and with a new iPad, I'm fairly certain you are going to need the current version of iTunes. However, in order to run the latest version of iTunes, you need to be running a much higher version of the OS - (like Lion or Mountain Lion), and I fear that your computer won't be able to run that higher OS version....
Another option for you would be to create an iCloud account. With iCloud, you should be able to download any purchased music that you currently have on your iTunes library.
Do you want me to send you the link for setting up iCloud on your iPad?
OK, links are below.
I was looking around during the "intermission", and even with iCloud set up (which I think you want to do under any circumstances - it is free unless you decide you want to purchase additional storage), you may not have access to your iTunes library. It seems you need, at the very least, a version of iTunes that requires Leopard to even be able to load it. And even if you were at that level of OS X, I'm not sure you would be able to get that older version of iTunes....
So even without the Music Library access issue, I don't think you will be able to sync your iPad for backup purposes with the OS X/iTunes levels you have, and with a computer that old, you probably can't upgrade to where you would need to be....
However, the good news is, that with iCloud, you do get much of your iPad data backed up to the cloud. So you would have that safety net.
If you can't access your music library, I'm still thinking that you may find that if you go into iTunes on your iPad, and select a song to purchase that you already have purchased, it may tell you that you have already purchased it, and ask you if you want to download it again. A little more cumbersome than just being able to click on a list of songs and download them, but still a way to get your songs on your iPad without having to purchase them again (fingers crossed).
So, here are the iCloud links:
Here is the "general link": http://www.apple.com/support/icloud/getstarted/
Here is the specific link for setting it up on your iPad: http://www.apple.com/icloud/setup/ios.html
Here is a nice overview of the iCloud features: http://www.apple.com/icloud/features/
So, take a look at those and see if you can get iCloud set up on your iPad.
Then, once it is in place and running, go into the "iTunes" icon on your iPad, and click on the Store. At the bottom, you will see and option for More...., click on that, then click on Purchased. Once you click on that, click on Music. On the next screen you will see an option at the top for "All" and "Not on This iPad". Click on the "All" one. If a list of songs comes up with a little cloud next to them, you are good to go!!! Just click on the little cloud to download to your iPad.
If you don't see any music listed under purchased, then click on the Music option at the bottom of the screen to go back to the store, then click on the Search option. At the very top, type in the song you want to "purchase", and see if you can find the exact one you originally purchased on your computer. Click on it, and then click on Buy. Hopefully, it will give you the "Already Purchased - do you want to download again" message....
If it doesn't, you may have to purchase your songs separatly for your iPad....
Just let me know if you need any help with all of this. It's a lot to take in!
Hope it works out in the best way possible!!!