How to sync my iPhone to a new computer?

I had to get a new computer and now I want to sync my iPhone to the new computer. I've researched online how to do this and gave it a go last night. I authorized my new computer, transferred purchases, and backed up my iPhone. However, when I went to restore backup I kept getting an error message. Is this normal? If I sync will I still be able to restore? I don't care so much about my music because that was all backed up and I was able to put that on my new computer, but I don't want my photos or contacts to be deleted when I sync. I do have iCloud, but honestly I really don't know how that works or how to put my contacts from iCloud back on my iPhone if they do get erased. Also, when I look at iCloud it seems to only have my contacts not photos or music or anything that like that. Thanks in advance for any help.

Added (1). The error message says: Itunes can't restore the iPhone because an error occurred.

The error you get would be helpful.

I used TouchCopy to transfer my all my iPhone content to my new computer as recommended here
https://discussions.apple.com/...s/DOC-3141

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