IPhone 4 Factory Unlocked Question

Question

I just Factory Unlocked my wife's iPhone 4 tonight from AT&T.  I think my wife plans on using her iPhone 4 on another GSM provider like T Mobile or something. After iTunes told me congratulations your iPhone is now Factory Unlocked I have a simple question.
Before I did all this I did Restore and Backup and now it is asking me if I want to Set Up as New iPhone OR Restore from iTunes Backup.
What are the pros and cons in either option?
If I restore from iTunes Backup will it restore it to AT&T or can my wife still use her iPhone 4 on T Mobile?
Or in order to use it on T Mobile do I have to Set Up as New iPhone?
I want to do the right thing.  If anyone has an answer to my question and is willing to share I would be most grateful

Answer 1

Thanks for the response Dave.
I looked at Apple's warranty for iPhone: http://images.apple.com/legal/warranty/docs/070808iphoneWarranty.pdf
It does say Apple may limit service to the country where it was originally purchased:
+Apple may restrict service to the country where Apple or its authorized distributors originally sold the hardware product, and provide warranty service at an Apple Retail or AASP location, where service is performed at the location, or the Apple Retail or AASP may send the product to an Apple repair service location for service+
It also says this:
+You may be responsible for shipping and handling charges if the product cannot be serviced in the country in which service is requested. If you seek service in a country that is not the country of original purchase, you will comply with all applicable export laws and regulations and be responsible for all custom duties, V.A.T. and other associated taxes and charges. Where international service is available, Apple may repair or exchange defective products and parts with comparable products and parts that comply with local standards.+
It does not specifically say that Apple won't service my iPhone here but it does provide Apple a leeway to make that decision.
I guess if Apple won't service it here, they will have to service it in Singapore.