Download the LM3914 data sheet; it has a wealth of information on applications of this device.
Up to ten LEDs can be used; twenty or more by simply cascading two or more LM3914s.
High sensitivity may be obtained as I did with a simple op-amp; the feedback resistor values in my circuit were for 18-30mV range but any other range can be obtained by changing values. The data sheet for the op-amp you use will help; Texas Instruments have wonderful application notes on op-amps.
My device had two adjustments, one for initial turn-on and one for final LED turn-on; each finished instrument was calibrated before despatch.
An alternative for your requirement might be a separate current and, perhaps, volt meter in a little case on your desk.
I recently built a little power supply;
using a small V/A meter from ebay. It's small because the raw DC comes from a laptop power supply; there isn't much inside the case.
All you would need would be a suitable meter or two in a small case; the ammeter would be of the separate-shunt kind to simplify connections. Shielded cable to the power supply should prevent any interference.