What bike+equipment for a long daily urban commute? In the (distant) past I commuted 6 km (more than half an hour) each way, on a cheap bike with big knobbly tyres.

Soon I'll have a new commute: 18 km each way, daily. That's much further than I've done in the past, and I don't want it to take 2 hours each way; but this reading suggests that it's feasible: 


  Most people who reside 10 to 20 kilometres away will also find it quite easy to cycle to work, although the distance in the high end of this range will become a little more demanding.


If I can do it in 80 minutes or even less each way, that would be ideal. I'm 49 years old, 6 foot tall, and weigh 170lb, and I want to commute by bike because otherwise I'd be getting no exercise in my week at all.

I've never bought or ridden anything but a cheap bike.

What equipment should I buy then, to commute 11 miles each way through a city (Toronto) on  flat, paved roads, shared with cars:


Wheels?
Tyres?
Clipless pedals and shoes?
Gears?
Handlebars (e.g. flat or dropped)?
Frame (size, shape, material)?
Mud-guard/fender?
Here I'll summarize everyone else's answers (because of all the Q+A scattered through in the comments), with some additional information that I got elsewhere from reading inspired by people's answers.


Wheels+tires: 700 x (28 - 38, maybe ~30), tires; slicks or light treads, not knobbly. The larger wheel makes it faster (because of 'gearing') and the ride a little smoother (because of the 'angle of incidence' when rolling over an obstacle). Possibly puncture-resistant tires, especially if you experience many puntures. Reinflate them weekly. With the narrower tires, beware storm drains, streetcar tracks, dirt roads, and cornering especially fast and on wet roads.
Clipless pedals and shoes: up to 35%-50% more efficient than without, but practice with them for 1/2 day to 2 weeks away from traffic first, because you must expect to fall off (everyone does). The normal type of clipless, for commuting, would be SPD: SPD are not impossible to walk in (unlike some other types). The stiffer the sole of the shoe, the better it distributes force over the whole sole of your foot. {Prefer a system which lets you clip onto either side of each pedal?}
Gears: multi-speed (e.g. 7, 8, or even 14-speed) internal-hub gears cost $300+ (which is more than derailleurs), and tend to exist only on more expensive (above $1000) bikes; internal-hub gears means lower maintenance, chain is less likely to fall off, easier to have a chain guard even, and you can change gears while stopped, maybe 2% less efficient that derailleurs, and takes a different kind of chain. Derailleurs are more common. A 2-position rather than 3-position derailleur on the front would be adequate if there are no hills.
Handlebars: as you wish (however, many/most people recommend flat instead of dropped); at commuting speeds it's more a matter of comfort than aerodynamics (and a more upright position is deemed more comfortable). Dropped affords more wrist positions; you can ask for interrupter levers on dropped handlebars, to access the brakes from more than one hand position/location.
Brakes: disc brakes work better or more reliably than rim brakes, especially when the road is wet (or the wheel isn't true); and if you go downhill at 70 kph you might want hydraulic disc and not just mechanical disk brakes (hydraulics are more expensive, are difficult or impossible to self-maintain, require less or no maintenance or routine cable adjustments, and require less finger-force to actuate).
Frame: not too important i.e. no-one offered advice on that; as long as (for speed) it's not a mountain bike, especially not a bike with suspension (suspension is inefficient). Aluminium isn't lighter than steel, because it's not as strong (and therefore there needs to be more of it). Aluminium is stiffer than equivalent steel, so (for comfort) higher-end bikes add (more expensive) carbon forks and/or seat posts to aluminium. Aluminium won't rust.
Other equipment: lights; fenders/mudguards; rack and/or saddlebag and/or panniers; bike lock[s] (maybe one chain and one U-lock: not a cable, which is easy to snip); maybe mirrors (you can/should shoulder-check as well, but many/most urban bike accidents happen while the rider isn't looking ahead); maybe a trip computer; a tire pump, able to inflate to about 110 psi (so not just a little hand-pump); bus fare (in case of a flat or irreparable tire, or horrific weather).
Store: find a "good" Local Bike Store (LBS), where you can meet the mechanics (a "good LBS for commuting" isn't necessarily the same as "good for road-racing" or "good for MTB"). Pretty much any decent LBS will allow ~30 minute ride: take a few for a test-ride, before you buy, to see which one feels right. Furthermore, expect to pay at least $600/year in maintenance costs (as much or more than the cost of buying the bike), visiting the shop at least 3 times/year: which is another reason why it's important to find a "good" LBS.
Speed: expect to average 20 kph at most, in the city, when there are stops and lights etc.
Cost: a decent $700 (including brakes and gears but perhaps excluding 'extras' like lights) bike from a good store should be "great" (but it won't have internal-hub gears, nor hydraulic disk brakes, nor any carbon components)


Additional comments or advice will be welcome.