We don't do specific product recommendations here on SE Bicycles, so all statements will be somewhat general and relatively opinionated.
For general purpose riding, you probably want a "Hybrid" bike. That's a diamond frame with flat handlebars, slick or semi slick tyres, and the ability to fit a carrier/rack and mudguards/fenders.
You don't need a racing road bike because they are expensive, have weight limits, and aren't particularly comfortable or versatile.
You also don't require a mountain bike or MTB. Suspension sounds like a good idea, but it saps your energy and is useless on sealed roads. If you end up getting a bike with front suspension, make sure you can turn a knob to lock it out.
As for your gears question... by your own statement you're out of shape. Get a bike with gears, this will lessen the impact of a climb on your body.
Specifically a transmission with a triple front chainring instead of a double. This gives you a "grannie gear" to slowly grind your way up anything a car can drive up.
At the back you're unlikely to find fewer than 7 gears these days, but the quantity doesn't really matter. More gears costs bit more. You'll need a larger number of teeth on the big gear. 32 or 34 used to be big, but some bikes can have as much as a 40 tooth. (This was called "megarange" by Shimano.)
Another option is an internally geared hub (aka an IGH) which could be anything from 3 speed up to 14 speeds. An IGH with 14 linear speeds is roughly comparable to a 3x9=27 speed, because of the overlapping ranges.
You can also find bikes with a "gearbox" in the frame, between the pedals. I am unfamiliar with these, they're not common here.
If you're convinced that a singlespeed is better, or you'd rather believe the singlespeed purity hype then remember back to riding in your youth. Would you have ridden up a hill in your flat-land gear? Why would you do that now?
You haven't mentioned a budget. Generally speaking, anything under ~$750 US new is likely to be a bit crap in the quality department, and heavy on rubbish like cheap suspension. If your wallet runs away at that bottom line, do consider a quality used bike. They can be had for much lower cost, and work just as well.
Budget for a lock or two, a helmet, and something bright. If you ever want to ride at night you need lights front and back. These add up too.