What to look for in a multimeter?
Accuracy. Which is something else completely than resolution. Your meter may have 4 digits, that's a 0.1 % resolution, but if its accuracy is only 1 % that last digit is useless.  

Accuracy is given by two numbers, an absolute error and a relative error. The relative error is the one expressed in %, like 0.5 %. The absolute error is expressed in digits, like 2 digits. If you have a 0.5 % meter, +/- 2 digits, that means that a reading of "100.0" may as well be (100.0 + 0.2) * 1.005 = 100.7. Engineers fresh from uni often neglect or underestimate measurement error due to the number of digits the meter gives them.

The absolute error becomes less important when the reading gets larger, like for a 900.0 reading 2 digits are relatively less (0.022 %) than for a 100.0 reading (0.2 %). 

RMS. If you need to measure non-sinusoidal waveforms you'll need that. Non-RMS meters assume your waveform is a sine, and will only produce correct results if it actually is.  

Autoranging. You don't want to put your probe aside all the time to turn the knob. 

USB interface. May sound as luxurious, but can be handy to log a whole series of measurements in the computer.