Q: i have a 3G phone and just got a new 5S do I have to save my contacts before I can use by new phone?

One option:

If you have iOS 5 or above installed on the iPhone 3GS, you can go to Settings > iCloud and turn Contacts on there. That will cause the contacts to be uploaded to the Contacts app at https://www.icloud.com/  On the new phone (using the same Apple ID for iCloud) you can turn on that same setting and that will cause the contacts to sync to it.

Another option, which will transfer more than just contacts: Transfer content from an iPhone, iPad, or iPod touch to a new device - Apple Support

Your contacts should be synced regularly to your computer or to a compatible cloud service if you're using the device as it's designed.