actually DDRYA,
though picture speak a thousand word, for the life of me i cant actually see what type of transistor ur using, whether the yellow wire on top is the positive or the negative side of the circuit. however about our question, usually when you are powering a project and want to switch on and of a solenoid it is always better that you make the connection parallel.So in that sense you could use a 12Vdc power supply but 14Vdc would be a better choice since there would be a drop in the transistor, however i would also warn you that the arduino have an absolute max Vdc input of 12Vdc.
So my suggestion to you is that,
if you are willing to use 2 power supply then,
1 7Vdc power supply for your arduino and 1 14Vdc power supply for your solenoid.
or
use a single 12Vdc power supply, is good for both.