You may want to look in to the Fluke 175. It can measure down to 10uA or 100uV, is true RMS, good for 600VAc or 1000VDc, can measure capacitance and has a nice 6000 count. It's considered the baseline Fluke for both higher end electrical work and electronics work.

The Fluke 179 is a little more expensive but also more accurate and has a backlight display with the same specs. The 179 would make a good, solid lab meter. For a little extra you can have it NIST traceable.

The only down side to the Fluke 170 series meters is that they do not have a peak hold.

http://www.amazon.com/Fluke-175-ESFP-Digital-Multimeter/dp/B00012Z0UM

http://www.amazon.com/Fluke-177-ESFP-Multimeter-Resistance/dp/B005WFW26S

On a budget the Extech EX330 for about $50 should handle your needs at a 4000 count. It won the EEvlog $50 meter shootout. I don't like how the voltage and fused milliamp receptacle is shared, I prefer a meter with four receptacles.

http://www.amazon.com/Extech-EX330-Autoranging-Multimeter-Thermometer/dp/B000EX0AE4

For a $100 range something like the BK Precision 2709B is nice with a 6600 count. I believe it won the EEVlog $100 meter shootout.

http://www.amazon.com/Precision-2709B-Auto-Ranging-Multimeter-Millifarads/dp/B004O8Z89C