Given the small area that car is running on in the video, I'd say it's using a 1.0 motor.
As to your questions:
Speed
Depends on which car you get. Tomy has 3 different motors they put in the different models (1.0, 2.2 and 2.6). The 1.0 is slow, but good choice for very small areas (like running on a coffee table). The 2.2 has good amount more punch and is better suited for bigger areas (like the floor or small to medium tracks). And the 2.6 (only comes on the 'special edition' car kits) is a little faster than the 2.2 and gives more of a racing feel.
That's the stock motors, there's other 3rd party motors too and you can go as high as a 3.8 Motor for some CRAZY speed!
Handling
In a word, 'Jerky'. Since these cars are so small, you can't exactly put a servo in there, so Tomy uses a magnet as a means of steering. when you press the steering button to the left, it activates the coils in the steering and pulls the magnet and forces the wheels to shift in that direction.
It's crude, but it works and with some practice you get used to it.
Costs
Prices range from a few dollars up to near the cost of the car itself. But for the most part, there's a TON of stuff you can get and the prices are low enough that it won't kill ya.
Bit vs DigiQ
Ha! I'm not opening that can of worms, you can find PLENTY enough talk and comparison within these forums for that.
My recommendation to you...Go ahead and pick up a Bit, at under $40 for a full kit you won't go wrong. Also, unless you're really limited with space, get a kit with a 2.2 motor (the 1.0 is just too slow).
Good luck!