Hooking up my iphone to a new computer for the first time....

Question

My computer broke and isn't worth fixing so I can't access it again. My mom just bought her a new laptop so I just inherited the one she had been using (actually ended up working out great for me cause it's only a year old and nicer than mine that broke).  My new computer didn't have iTunes on it until I just installed it a few moments ago.
My question is whether or not I need to be concerned that my iPhone is gonna be erased the first time I plug it into this new computer?  I'm concerned I'll lose all my contacts, apps, photos, settings etc.  Just last week I backed up all my music and movies to my external drive, luckily I happened to do that right before the computer died so I'm not worried about that. 
If it is a problem how do I stop it from erasing all that when it syncs? 

Answer 1

In regards to iTunes content, an iPhone can be synced or manually managed with music and videos with an iTunes library on a single computer only, and photos can be transferred from a single computer only.
When transferring iTunes content and photos from another computer, all iTunes content and photos transferred from a different computer will be erased from the iPhone first.
Photos transferred from your computer are optimized for viewing on your iPhone as part of the iTunes sync/transfer process. The original resolution of these photos is reduced on your iPhone. All photos on your computer and all photos transferred from your computer to your iPhone should be included with your computer's backup along with all other important data, which should include your iTunes library as well.
Backing up your iTunes library per the instructions included with this link and transferring the backup to a new or different computer will prevent any iTunes content from being erased from your iPhone first when transferring iTunes content from a new or different computer.
http://support.apple.com/kb/HT1751
iTunes includes an option to transfer iTunes content that was purchased/downloaded from the iTunes store from an iDevice but this is for iTunes content that was purchased/downloaded from the iTunes store only.
First you need to authorize the new or different computer with your iTunes account with iTunes if you haven't already done so. With your iPhone connected to iTunes and without syncing, at the iTunes menu bar go to File and select Transfer Purchases From - the name of your iPhone.
You can use a 3rd party paid utility such as this one to transfer photos from your iPhone that were transferred from your former computer, but the original resolution of these photos will be lost, and such utilities are not supported by Apple.
http://www.ecamm.com/mac/phoneview/
Contacts are designed to be synced with a supported address book application on your computer. If you aren't doing so, contacts on your iPhone are not touched when syncing your iPhone with iTunes on a new or different computer. If you are syncing contacts with a supported address book application on your computer and the supported address book application on the computer is empty, before the first sync for this data enter one contact in the supported address book application on your computer. This will provide a merge prompt with the first sync for this data, which you want to select.