Can I sink my iTunes music library, and apps to my new computer?

My family just bought a new computer and sold the the old one with my whole iTunes on it! Now I'm afraid that I wouldn't be able to get any new songs or anything on the new computer. If I automatically log on to iTunes with my Apple ID with the new computer will it remember and sink all my data or can it sink my data from my iphone to the new computer? My question is is there anyway to sink my iTunes library to my new computer including apps and music

If you have songs bought from iTunes, then you can just download them again for free on your new computer.
You will have to sign into your Apple account. And I think you mean "sync", and yes, but you will have to download your app/song again, but if you've already bought it, then it's free.
So if you buy a song on your iPod, you can get it for free on your computer from iTunes.
But you have to remember your Apple ID.