Sync your contacts with your Google account and then when you sign into your Google account while setting up the new phone your contacts and anything else you sync'd to your Google account on the old device will sync to the new device from your Google account.
Go to the phones settings menu and scroll down to accounts.
Then click on accounts and then on Google.
Next click on your Gmail address / account and a check list will pop up. Check off what you want to sync to your Google account and wait for the spinning arrows to stop on each one you checked off.