Your choices for buying a quality bicycle are far better today than a decade ago, and light-years better than 20 years ago. Twenty years back you could either buy a road bike or a mountain bike. That was about it. Today there are so many variations it would be hard to list and describe them all.
I'll start with the road bike. This is what people used to call a "ten-speed," but you'll really be dating yourself and showing how out of touch you are by using that term, so stick with "road bike." The purpose of a road bike is to go fast. Period. It's light, the handlebar position puts you in a more aerodynamic position, and the tires are narrow to reduce rolling resistance. This is the bike for fast weekend rides with the local bike club. NOT the comfortable cruiser for around the neighborhood with the kids. Road bikes will come with anywhere from 18 to 30 gears, depending on the model and sub-category.
For a while the mountain bike was the bike people bought if they couldn't stand the uncomfortable position of the road bike; but then, those were the only two options. While mountain bikes are okay for around town riding (especially if you have heavily potholed or bumpy brick streets), they are really built for rugged unpaved trails through the mountains and woodlands. If you are interested in riding those rugged trails, but also want to have just one bike that will also take you around town, the mountain bike will do well. They come as either "full" suspension (front and rear; shown above), "hardtail" (front suspension only), or "rigid" (no suspension). A "hardtail" with smooth tires for the street can be a very good around town bike, especially with a rear carrier rack. Changing from smooth street tires to knobby trail tires can be a hassle; some riders have a second wheel set built for the second set of tires; changing wheels is easier than changing tires, and a second set of wheels can be cheaper than a second bike (and take up less room). Full suspension bikes are generally not so good for around-town use, because you can't mount a good rear carrier rack (unless you want spend over $100 for one made for rear suspension.)
A broad range of bikes called "comfort" or "hybrid" or "urban" bikes combine elements of road bikes and mountain bikes, and often do so with a more upright seating position. The tires will be midway between road and mountain; wide enough to handle a little dirt and absorb some road shock, narrow enough to give reduced rolling resistance. Some are now being built with 7- and 8-speed internally-geared hubs instead of the derailluer and cog system found on most bikes. These internally-geared hubs are very user-friendly, enabling you to shift while stopped, and freeing the rider from worrying about a chain that might derail from the cogs or chainrings.
"City" or "commuter" bikes are finally catching on with US bike companies. Similar to the "urban" bikes above, they go a step further and provide accessories that help make cycling a practical mode of transportation: rear carrier rack, fenders, kickstand, and sometimes a chainguard and front and rear lights.
If just want to keep it really simple, there's nothing wrong with a good ol' cruiser. Most are single-speed with coaster brakes, but some have internally-geared hubs and handbrakes. If style is your primary concern, there are tons of options available today.
Lastly (though there are still plenty more types of bikes I could be covering here -- I'll get to them all eventually!), there is the recumbent. If comfort is your primary concern and you don't have plans to ride those rugged mountain trails, this is the bike for you. You sit in a real seat, and pain to your hands, arms, neck, back, butt and (ahem) soft tissues are concerns of the past. As with so many general bicycle types, they also come in a variety of sub-categories: long-, mid- or short-wheelbase; under or above the seat steering; varying seat angles and heights; even three wheel versions.
In a future post I will cover some of these options in greater detail; especially urban and commuter bikes. Then there's always fixies, tandems, touring, cyclocross, choppers, crank-forward bikes, folders, travel bikes, long-tails, cargo bikes......better get a bigger garage!