The important thing is to get thick enough wire for the current it has to take, which
means once you know the lengths of the runs and the current each run takes you
sit down with ohms law and determine the max acceptable resistance for each run and
then the max acceptable resistance-per-unit-length of the wire.
You also separately have to check that the wire can take the current without overheating.
The first calculation is to avoid the bulbs being too dim due to resistance in the wire,
the second to avoid the wires being too bright!
Half here are suggesting solutions for actual incandescent light bulbs, the rest want to know which LED (s)?
I want to know precisely what you're powering I'm guessing you bought screw in 110/240vac bulbs complete with driver for the led ... if so you can't place them in series...
Neither method wil work for bare LEDs. Either wire them in series and use one current regulator or use a current regulator for each and wire the current regulators in parallel. If you put parallel LEDs on a single current regulator they will not share the current evenly and some might overheat and die, dumping more current on the other two.
With a fixed voltage supply the 'current regulator' can be as simple as a current limiting resistor.