I built the “Joule Thief” circuit in this Youtube video by Xee2 / Xee2vids. This uses a Radio Shack Cat # 273-1365 transformer, an E13007 transistor and a 51 ohm resistor. He also puts a 200uF capacitor across the resistor and a 14 millihenry choke in series with the resistor. The 120VAC primary is turned around and becomes the secondary, driving a 120VAC LED light bulb.
I used the same transformer, a 47 ohm wirewound resistor, a 220 uF capacitor and the same 40 turn inductor using the same toroid no longer available from Goldmine Elec. I used a 2N3055 transistor, mainly because I could see no reason why the E13007 would be better than the 2N3055. The voltages on the transistor are very low, less than 12V. The E13007 is made for much higher voltages, the 2N3055 can handle 60 volts; both far exceed the voltages in the circuit. The average experimenter is not going to be able to find the E13007 as easily as the 2N3055.
The LED light I used was the Lights Of America 2325LEDE12-LF4 2 watt, 110 lumen, 27 LED candelabra base light. It lights up nice and bright in the circuit.
I varied the supply voltage from 1.5 to 5 volts. The supply current changed from about 450 to 600 mA from 1.5 to 2.25V. Above 2.25V to 5V it changed only slightly above 600 milliamps, uncharacteristic of a typical JT, which would vary from low to high.
I shorted out the choke and the light brightness didn’t change, but the supply current went down a few tens of milliamps. From that I came to the conclusion that the choke really was not necessary..