If I sign up for service in store, will I have to pay my first bill then and there?
That depends on a lot of things - your age, your credit history - are you porting in from another carrier? taking over an existing Verizon line via Assumption of Liability? Moving from pre-paid to post paid? Starting a brand new, never had a cell phone account?
Most likely you'll have to pay something - the device cost, taxes, accessories (if chosen), but the actual service portion is billed.