For example, how does price vary with precision, speed, reach and
The price vary a lot, from a couple of hundreds of bucks to hundreds of thousands of dollars ( Willow Garage's the one-armrobot PR2 costs \$285,000 and The two-armed costs \$400,000 ), it goes up- as you can guess- whenever the robot arm is precise, fast, long, strong, collaborative (i.e. designed to interact with its environment), or have more DoF's (Degrees of Freedom). Also, take into account the flanges, tools, the palette of software they come with, certifications, etc. It really depends.
Is there a database of industrial robot arms including information
like the price, precision, speed, reach and strength of each model?
I don't know of such a database, but you can find all these information (except prices, these companies are pretty secretive, they usually reveal it to potential customers. I work on KUKA's robots in my company, I didn't know about their price until our PR told me about the deal) on the Robot's manuals available on the companies' websites.
If you want to narrow down your choices, check what's available on the applications you want your robot to perform (if the robot will do repetitive work inside a confined space, there's no need to buy an expensive collaborative robot). I think, the big guys in the industry like Kuka, ABB, or Fanuc have a complete range of robots for different applications and at different sizes.
Check this link out: