I have looked at the datasheet of the transistor too, in order to check for Icmax, which is 200mA. I have calculated Ibmax at beta 20 and got 10 mAmps and at 6 volts I get that I need 600 ohms resistor.

So thought using something like 300 Ohms(the closest to 600 I had) will be okay, also I have 2 kOhms but I am afraid that this might let too less current in the base

The problem though is that the led is not being lit/glowing.

Am I wrong in the calculations ?

Datasheet that I have used: http://html.alldatasheet.com/html-pdf/11470/ONSEMI/2N3904/365/2/2N3904.html

Can you please tell me if I have made some of the readings wrongly(Vbe = 0.65V, Icmax= 200mA, hfe= 20, should I always take the lowest value of the hfe to determine resistor on the base) ?

The circuit that I have realized already in physical model on breadboard:

P.S. I have tried the same with 2 kOhms resistor(just from desperation, thinking that I give too much current with 300 ohms and this might fry the transistor) The result is the same(the led or the load in the case is not being lit)

Also if you know good books about transistors, their working and formulas explained simply, I am open for suggestions(the articles are not enough in-debt).