Hello. My name is Michael. I can help you with your question.
On Android devices, you shouldn't have to be concerned about syncing the contacts directly between devices as long as you have a Google account that you used on the i9000. When you set up the i9300 and enter your Google Account information (as well as other accounts), the information from those accounts should synchronize automatically, particularly contact information. So I would suggest starting with just the Google account - the contacts should be in "the cloud" so you shouldn't have to rely on anything on your PC.
However, if you HAVE done a backup to your PC of the previous device, and you know how you backed it up, you can use that to restore items to your new phone - it's just not the easiest way to accomplish the task - and you DO have to know how you backed it up. If you can tell me how you backed it up, I can tell you how to restore it. If you're not sure, or if you didn't back it up to your PC explicitly, and your contacts exist in SOME account (even if it's not Google) - if you tell me what type of account that is, I can tell you what you need to do to get them from there to the device.
The Google account applies to any programs that you have purchased or downloaded on the first device as well. You must be logged into the i9300 with the new device to use those programs even if you could restore them. Fortunately, if you are logged into the same Google account, you don't even have to go through restoring the programs - you can just go to the Google Play store on the device and download them again to install - if you've paid for something under that account it will still be available to you on the new device. Just go to the Google play store on the device or, once your new device is registered to your google play account (which happens automatically when you set it up), you can go to the store on your computer and select what you want to install to the new device:Google Play Store
Finally, to transfer other items, like pictures or personal documents, the easiest solution is something called "dropbox". Since your phone has the ability to share via dropbox, all you have to do is set up a free dropbox account. Once you do this, you can put items in it on your computer and they will show up on your phone.DropBox
Please let me know if you have any questions.