Just about any adult-sized bike without suspension can handle a 300 lb rider. I don't think most bike companies list weight limits because of liability issues.
The reason people recommend bikes from the bike shop instead of the department store is that they're made to hold up better to regular riding. My first bike as an adult was a Huffy comfort bike, and it was very comfortable to ride, but I kept having to replace things like pedals and brake cables. Then things started to break on it that I couldn't fix, and by the time I'd had the bike 9 months it had to be replaced. By contrast, the bike I have now is an Electra and I rode it 5 days a week for a year and three months before anything needed fixed on it.
You'll be better off buying a good used bike from Craigslist than a new department store bike. Cruisers aren't the only bike with an upright riding posture, there are also hybrids and comfort bikes.