Synching iPhone with new computer. Will I lose anything?

Hi guys. I recently lost my computer whilst on holiday and have recently purchased a new one. I am looking to connect my iPhone 4 to my new computer but I am worried that I will lose everything which is on the phone already. When I purchase an app, for example, on my iPhone, does that need to be backed up on my... show more Hi guys.

I recently lost my computer whilst on holiday and have recently purchased a new one. I am looking to connect my iPhone 4 to my new computer but I am worried that I will lose everything which is on the phone already. When I purchase an app, for example, on my iPhone, does that need to be backed up on my computer or is the purchase saved in my account so I won't have to purchase it again? There is a section for sync purchases so do I have to do this to keep everything safe?

I think I have also reached the permitted amount of computers you're allowed to sync your iPhone with and therefor have I deauthorise one. Does anyone know if this has any affect in my content?

Thanks in advance for your replies!
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