This article explains how to back up your phone, then restore the backup to your new phone to transfer your data and settings: http://support.apple.com/kb/HT2109.
You can use the same sim card if it's the same carrier and a compatible size. You would need to contact your carrier to have the service transferred to the new phone.
It should include everything. To be safe, I would create a backup on your computer too (go to the Summary tab of your iTunes sync settings and click Back Up Now; also go to File>Devices>Transfer Purchases).
Also, sync your data to your iCloud account (contacts, calendars, etc.). When you sign into your iCloud account on the new phone your synced data will appear on it.