Youre saying an iTunes account to buy music and stuff?
Yes - you need an iTunes account to purchase music and video from the iTunes store, and the same for paid or free 3rd party apps from the iTunes app store.
You need to create an iTunes account with iTunes on the computer you will be syncing your iPhone with for iTunes content. In regards to iTunes content, an iPhone can be synced with an iTunes library on a single computer only. I suggest syncing iTunes content with your computer at home. The iTunes account you are logged in with iTunes on your computer will be transferred to your iPhone when syncing. This will provide for being able to purchase and download music and 3rd party apps from the iTunes store with your iPhone. When syncing your iPhone with iTunes after doing so, any music or 3rd party apps purchased with your iPhone will be transferred to your iTunes library on your computer.