They have their uses but for most things a cheap digital multimeter is well worth the investment.
I quality analog meter (I'm talking something like a calibrated Simpson) is damn near worth it's weight in gold; one thing it can show which a digital meter can't (barring some expensive models) is AC "ripple" on a DC voltage. One of these days I'll have my Simpson, I swear...
With a moving coil meter you must be sure to connect the probes the right way round as it can't measure negative volts or current (whereas a digital meter can).
Well - not easily; if you know that the voltage will be negative, you just swap the probes around. Otherwise, you could add on a DC bias battery and/or adjust the meter centering potentiometer to put the needle in the middle of the meter for "0 volts", then you have half the range on either side for positive/negative measurement.
ALSO for the first attempt at measuring current just connect the probe briefly so that, if the current is too high and drives the meter right off its scale you can disconnect quickly before damage is done to the meter. Most digital meters have a 10 amp setting which you would use first to make sure you were not going to damage the meter when using the low current setting.
Actually, if you are completely unsure about the maximum of anything (current, voltage, resistance) - start with the upper range setting first, and work your way down. In the case of current, if the maximum is potentially way above even the highest current setting, then the best way to measure is to use a current shunt resistor and measure the voltage drop across it, then use Ohm's Law to calculate the current from your measurement and knowledge of the resistance (a cheap current shunt resistor can be made with a piece of thick solid core AC house wire; you can find the resistance for the gauge and length via several online tables - there's also plenty of tutorials on how to build your own shunts - but if you can afford one, a purpose built high-current shunt can be very useful; the wire they are made with is designed to not change in value under testing or temperature, but they can't be kept in continuous operation - they are only meant for testing).
Also - as a note to the OP - if you need to plug into the high-current jack of your meter, make sure to always unplug the lead and plug it back into the "standard" settings jack before measuring anything else - if you don't, and you attempt to measure a voltage, you'll damage the meter.