I got back on a bike just over 3 years ago after having not been on a bike since probably the mid 90s, when I was in my late 20s. The expression "just like riding a bike" was oh so true.
A hybrid or a cruiser bike would probably be a good fit for you. I still marvel at how far technologically bikes have advanced from my 1986 Schwinn World to my 2008 Kona Dew.
Avoid toy store and department store bikes. By some estimates, they are engineered for a useable life of 70 miles before they hit the landfill.
You definitely want an actual local bike shop, or LBS. It will be a little pricier than toy and department store counterparts, but wear, tear, and tune-ups will eat up that difference in no time. In the end, toy and department store bikes are way more expensive.
Contrary to mythology, you don't have to spend thousands on a bike at an LBS. My Kona Dew was $400. A toy or department store hybrid would probably run $250 to $300, but at $70+ a pop for tune-ups, maintenance (I'm a commuter so I ride in shitty weather), help with accessories, etc. I saved buying from an LBS.
With a hybrid you will definitely have gears, but there are single speed cruiser bikes. If you go cruiser, I would still opt for a multi-speed cruiser, at least 7 or 8 gears. For a cruiser, I really like the Electra Townies and Cruisers.
http://www.electrabike.com/Bikes/townie-bikes-electrahttp://www.electrabike.com/Bikes/cruiser-bikes-electraHop over to bikeforums.net and sign up. Lots of very helpful and knowledgeable folks there. Ask about a good LBS in your area. Maybe ask in the Southeast Regional forum about a good local LBS
http://www.bikeforums.net/forumdisplay.php/234-SoutheastThere are lots of posts with recommendations about good bikes to suit your needs. Kona Dew also shows up on a lot of lists as recommended. Pic below.
Ideally, your LBS should be close enough for you to ride there. If it's close, you can always stop in and get help with stuff more conveniently.
Finally, North Carolina appears to have a lot of bike clubs throughout the state. NC DOT has a lot of good info online about clubs, LBSes, routes, maps, etc. Maybe find a local club and check 'em out. Get some local assistance in picking out a good bike for you.
http://www.ncdot.org/bikeped/bicycle/bikeclubs/http://www.ncdot.gov/bikeped/bicycle/bikeshops/