I recently saw a post regarding propeller quality and I figured I would contribute my motor-selection knowledge as a nice complimentary post.
This is my first post, so a quick intro. I'm an electrical design engineer for BLDC drives, known in the RC community as ESC's. Most of our applications involve fans and pumps, so there is a lot of similarity in what I do in my day job and what you all are doing here. I found DIY Drones a few months ago and I now catch it nearly every day looking for something interesting. I always find something :). I will be doing my first UAV soon with the standard (for many of you) Bixler drone. It is on its way :).
Now, to my topic. Above, I have a very typical series of curves (credit to these guys for the chart). These curves are generated by applying a constant input voltage to the motor and ramping the torque from 0 oz-in to locked-rotor.
There are two ways to choose a motor. For performance, you would want to look at the power vs. torque (dotted red). In this case, you would want to choose a prop that places about 0.325 oz-in of torque in order to maximize the power output of the motor.
The second way to choose a motor, which applies more to drones, is to look at the efficiency curve and to select a motor/prop combination that puts you just to the right of the peak efficiency point. In this case, a load of about 0.1 oz-in would be ideal. If you select a point to the left of the peak, even light variations in load will cause vast efficiency swings (notice the steep slope) and if you select a point too far to the right, then you will be losing power continually with little recourse.
One more thing. If the voltage (PWM duty cycle) is reduced, these curves also scale to the left. The scaling isn't perfectly linear, but it is close enough for estimation purposes. Also, your propeller draws torque in a very non-linear fashion (vs. speed). It is *very* likely that your max efficiency point with a particular motor/prop combination is not at maximum throttle, but at some other point. So you might need to do some testing on your current setup to find out where you are and go from there.
It is likely that you don't have a dynamometer (test equipment that records torque and speed by applying a load to a running motor). I certainly don't, but I do know that there are ways to make a DIY version. Most motors on the market have a torque/speed curve like the one above, or maybe enough data that you can generate a rough estimate and draw a graph using Excel or LibreOffice. Basically, torque/speed curves are attainable from the manufacturer.
The prop is a different story. Each prop does have a typical torque applied to the motor vs. the prop speed... but I can't seem to find one. This might be b/c a prop behaves differently at standstill and while moving, but it would still be nice to have a starting point. The ideal way to get this would be to get a torque transducer and simply run the prop through its speed range. Unfortunately, that is expensive. This is where our motor torque/speed curve comes in again. Note that one of the curves is current vs. torque (blue). You should be able to measure the DC current draw of the motor and get an idea of the actual torque being applied to the motor shaft. It would be best to take this measurement in-flight, but a static thrust shouldn't be too far off the mark. Remember to keep the voltage steady at the voltage at which the curve was taken. These curves are only valid at one particular voltage!
Now that you have the torque, go vertically on the chart to the motor efficiency to see where you are on the efficiency curve. At 100% throttle, the ideal point is just to the right of the peak efficiency for maximum endurance or the peak power point for a performance or aerobatic design. Or you might decide that you want to run at some other operating point for most of your flight, in which case, you would want to choose a motor/prop combination that puts you in that sweet spot. I would stress that you want to be just to the right of the peak. To the right of the peak, efficiency drops off slowly, so a small error won't cause a big loss. To the left of the peak it drops off very steeply. Manufacturing variations, measurement errors, etc. will likely add uncertainty to your data, so be sure to stay in the safe zone rather than on the edge of the cliff.
There are loads more to this. People have written PhD's on several of the topics touched here and my knowledge only scratches the surface, however, this should help you make a more informed motor/prop selection.