It is rare to use simple LED's normally LED's are sold as a unit complete with some current limiting device and so if the voltage is correct and the current available is greater than required no problem.
However if you are talking about an LED without some package then current is all important so a 3mA LED must be feed with 3mA or less. The voltage will be some where near 2 volt but it's controlled by the LED it's the current which matters.
When controlling a LED we use a driver these will deliver a set DC current.
But normally we would use a DC power supply and inside the package of the bulb there will be a current limiting device could be a simple resistor or it could be a switched mode current regulator it could even over drive the LED by giving it pulses of power.
I would guess you want a simple DC power supply. Using a LED package on AC is a problem as even with a simple transformer the peak voltage is above the RMS value and with a switch mode the spikes could be well above the RMS value. There may be a full wave rectified soothing package built into the bulb but we simply don't know so one make of bulb may work A1 and another fail premature.
The major problem is manufacturers have tried to make things simple naming devices after the device they replaced but have as a result given us a selection of names which may not match the device supplied.
Transformer is a simple wire wound device to isolate and supply a voltage in relation to the input voltage the output is as a sine wave.
Electronic transformer is however an electronic device which turns AC to DC then back to AC at high frequency transforms it to approximately the voltage requires and changes the mark/space ratio to give a RMS output of a very well regulated voltage but the peak voltage could be very much higher than the RMS OK with tungsten bulb but not a LED.
A driver has a current controlled output but many lighting manufactures label simple DC power supplies with a constant voltage output as drivers.
My MR16 bathroom lights have a toroidal transformer and in theroy fitting 12 volt MR16 LED lamps should not be a problem. They did work for a time then one by one the LED's failed clearly the peak voltage was a problem.
So if they say 12 volt then unless it states AC consider it must be a smooth DC voltage. And as longer as load (Lamp Wattage) is between the minimum and maximum stated then it will work. (Switch mode devices often have minimum as well as maximum)
If it says 350 mA then it needs a constant current driver with a 350 mA maximum the voltage could be 2 volt or 24 volt it's the current that matters.
Because we buy 12 volt 7W MR16 bulbs which have the current control built in it is easy to think all LED's are like this.
I show a 1W 3.2 volt 350 mA LED you could have 1 to 8 of these driven in series from a 350 mA 24 volt driver but
This Driver would supply two series strings 8W each so 16 of the LED's shown which is a very different set up to using the LED's already supplied with heat sinks and drivers and a 12 volt DC supply.
