Well to begin with, remember the term "ten speed", it used to mean that a bike had ten possible gear ranges. It really doesn't mean that anymore. Today when someone talks about the number of speeds a bike has, they usually mean the number of gogs on the back wheel. A cheap x-mart bike will have 7. Abike shop bike will hav 8,9,10 or, 11 cogs in the back. And two or three in the front. Look for a bike with 8 or 9, they will have gear ratios that are closer together, so when you shift you won't experience a big jump in effort.
The term "hybrid" has a wide range of bicycles to near mountian bike, to almost a road bike. From sitting upright, to a road bike with flat bars instead of drops. So shop around, look at lots of bikes, and shops(please go to a bike shop).
Frames come in different sizes, no matter what the wheel size and bike type, get a frame that fits. The 27 inch wheel is rare on a new bike, most will have 700c.
Remember toe clips and straps on your pedals? They have been replaced(for most of us) with clipless pedals. They are like a tiny ski binding built into the pedal, with a cleat on the shoe that engages the pedal. But that probably down the road aways if you decide to try them.
But again most of all is the bike fit. A bike that fits will be comforable to ride, and so you'll want to ride it, and you haven't wasted your money. One that doesn't fit, you won't enjoy riding it, so you won't.
Riding is supposed to be fun and enjoyable, don't worry about how fast you go, or how far, just Enjoy the Ride.
Good luck, and lets us know what bike you get(then we'll tell you about the n+1 requirement).