Most commonly recommended mounting method for a flashlight is using lockblocks by
TwoFish. This is a product originally marketed for mounting a u-lock to your handlebars. It's basically a rubber block with a couple of velcro straps. One strap goes around the handlebar, the other goes around the light. Pressure on the rubber block keeps it from shifting around.
You generally get pretty good results with a 2AA or smaller light. Larger lights
can be made to fit, but you'll find they'll bounce around a lot more.
You're right that flashlights tend not to have as long a runtime as dedicated bike lights. Part of that is the battery pack, part of that is the strength of the light. It's not that the Cateye is necessarily more efficient than a flashlight is, it's that it's running at a lower power. Also, many manufacturers (flashlights as well as bike lights) tend to be overly optimistic on battery life - using ratings literally till they fade into nothingness. A common practice on the flashlight boards is to consider battery life as rated until the light fades to 50% power - a much more useful number.
Dedicated bikelights have their own mounts, often featuring quick release so you can take the lights with you when you park them. They also usually have a blink mode - many flashlights do have this as well, but they're often on higher priced multi-mode lights.
For short-midlength commutes a 2AA light serves quite well - especially when paired with a long-running blinky light like a Planet Bike Beamer5. Solid light to see the road and to provide a reference point for vehicles, blinking light to get attention. Particularly with the AA's you can run rechargables which both gives you better runtime (usually) and eases the hassle of buying alkalines every few days.
One downside to using rechargables is that with many lights, you get little warning when they run flat. Unless you have a routine down where you know when the batteries tend to go and recharge them before that point, you might get surprised because NiMH's run pretty strong until they're nearly exhausted - unlike alkalines which gradually fade the whole way.
On a fairly well-lit commute through the city, the blinky can be your backup light. My wife carries a second flashlight as her backup - each with their own lockblock so she can use both on a really rough night when she wants extra light.
The Inova Bolt 2AA / Beamer5 combo has run on my wife's bike daily for around two years without fail, so I have no problem recommending it. Others can chime in with other lights they've used (I have no experience with any other than the Inova on bike duty) - I often see Fenix coming up, but they're close (or over) $50 usually. Like I said, I'm trying a new Coleman light this weekend, so I'll be able to see at least if it flickers or something bad when on a bike.
Taillights, yeah most of us use red blinkies. Most common ones I see recommended for brightness are Planetbike Superflashes, Blackburn Mars, and Performance Viewpoints. The Dinotte is a whole 'nother breed - basically it's a flashlight-caliber red light, but it's also much more expensive than the others, so it's your call which way to go. My wife runs a Mars because it mounts on her bike better. I have two Viewpoints - one on the rack trunk, the other on the helmet.
Hope that helps!