Why is the collector and/or the base current of a transistor independent of the voltagesource of the collector?
The formula \$I_c = \beta I_b\$ applies in forward active operation of the BJT. But to minimize heat dissipated by the transistor in this circuit, you don't want to operate the BJT in forward active mode. You want to operate it in saturation mode. Do this by increasing the base current (by reducing the base resistor value) until the collector current required to maintain forward-active operation is more than the 9-12 V source can supply.


  What would happen if I choose 1.5v, 5v, or 12v etc ?


The BJT isn't going to produce a negative voltage on its collector. So the voltage applied to the load (solenoid valve in your case) will be equal to the source voltage or less. If you use a 1.5 V supply, then only 1.5 V can be applied to the load. 

So choose a supply voltage equal to what is required to operate your load, plus a small allowance for the saturated collector-emitter voltage of your BJT.