The 328i, even in automatic form, would be a significant step up in performance over your 318ic.
Looking at the ad, it is not a good sign when the seller say the car has a V6. BMW has never made a V6, and the inline six is considered by most to be the very essence of BMW.
The dealer seems to deal primarily with domestic trucks, based on their inventory. I would suspect this car came from an auction. That said, if the car has a clean title and is mechanically and cosmetically sound, it would be a good choice. However, you need to have a good dealer or Indy mechanic look the car over before you buy it. I would be somewhat concerned about the mileage on an automatic transmission, as they have not been known for their longevity, and I would expect the car has its original transmission. Service history would be very important. Well-kept, these cars last a long time, but if they are abused they can be very expensive to own.
The price seems to be decent, even with 120k miles. I am generally reluctant to buy cars from 'used car lots' that are not a part of an established new car dealer, but I would not rule it out entirely.