What can you tell me about Mopeds vs. Cars?
My take on a moped for your purposes is don't do it. I'm not suggesting a large motorcycle by any means, but to do what you want, I'd be thinking a scooter, perhaps in the 125cc range (depends a bit on speed of the traffic on your usual routes, traffic, etc).
I'm a long time rider, and probably one of the scariest things I ridden, many years ago, was a moped. Why? Too slow to get out of the way of traffic, and to fast to be comfortably ridden on the shoulder or hugging the road edge bicycle style.
For a trip of 15 miles each way, in traffic, an electric is not even a consideration in my opinion.
Safety? Just like any two wheeler: tangle with anything with 4 or more wheels, and you will llkely lose that contest.
Mileage? My father in law has a 125 Yamaha Vino and claims to get better than 100 mpg. He's in his 70's BTW and bought the scooter for the purpose of saving gas while running trips much like what you describe.
New or used? Depends - use your best judgment. You should be able to pick up a scooter or small cycle that someone bought and decided they wanted something faster or larger and traded in at a nice discount. Also, dealers may have a new last-years model or two hanging around that would be a bit cheaper than the latest and greatest.
In any case, whatever you decide to ride, get some training, wear proper gear, and ride safe.
Quick edit: a moped in most states cannot exceed 50cc and most are capable of speeds on level ground around 30 mph (not 55 as the other poster suggested). A moped, has pedals as well, often used for starting, and for a little additional power going up hills, etc.