perimeter wiring LED lights thru pipe fence
Depending entirely on what the LED you insert is, the BEST way to do long runs of LEDs is to put them in series and run the required DC current through the system at whatever voltage that requires (the LED supply will be controlling the current closely in that case, the voltage will be what's needed to run the current.) But that requires that you use LEDs that are "bare" in the sense of having no attached/built in power supply.

If you are using 120/240VAC LEDS (which are low-voltage DC LEDs attached to a power supply which uses 120/240VAC and does the conversion locally) then you will perforce be wiring in parallel at 120/240V.

16 9 watt LEDS, assume pessimistically that they are quoting LED power use and ignoring losses in the power supply, say 80% to be pessimistic about power supply efficiency, comes to about 180 watts, should run 5.5 hours on a kilo-Watt-hour (for your pricing) and draw 0.75A on 240V or 1.5A on 120V. At 12 hours per night (average across the year) and 15 cents a kilowatt hour, about $120/year.

Assuming that your wire is rated for use in conduit/wet locations, likely won't be a problem, though it will obviously be better on 240V (less current for the same power, so less voltage drop.) If you have 12/2 UF wire that will be true, if you have 12/2 NM wire it is absolutely not true, and a code violation. I'm not going to bother sorting out the actual voltage drop from distributed lights (which will be less), but treated as a lump load at the end of the wire, 0.75A at 240V on 1000 feet of 12Ga results in 3% drop, so you would be fine. If dividing into two 8 light circuits, you'll be fine on either voltage.

How much you'll annoy your neighbors (especially if any of them like to look at the stars) is a whole other question.