Which servo motors for a precise but not powerful robotic arm?
You might start with motors made by the Swiss manufacturer Maxon. They're used in high-end robotic arms. They're expensive when bought new, but you might be able to get them cheaper off Ebay if you just need a few.

You should also think about how you will measure position and connect the motor to the arm. A lot of your position error will be in the backlash in the mechanism you build, error in the position encoder, and flex in the arm itself. You might also google "harmonic drive" or "anti-backlash gears."