Conditions for free radical bromination using NBS and peroxides?
From practical experience, I can tell you that the answer is "All of the above". 

First, your peroxide initiator needs some energy to undergo homolytic cleavage. This can either be achieved through UV photolysis (A) or heating (B). 

$$\ce{RO-OR &lt;=&gt;[h\nu][\mathrm{or\ }\Delta] RO. + .OR}$$

The amount of energy needed will correlate to the strength of the O-O bond. The energy available from UV irradiation is dependent on wavelength because $E=hc/ \lambda$. The amount of energy available from heat is dependent on temperature. 

I've initiated NBS reactions both ways, but I prefer heat since I can more easily heat a larger vessel.


  What about solvent polarity?


Solvent is the tricky point, and depending where you are in your studies, you may not have covered the other things that NBS can do. Under the right circumstances, NBS is also an electrophilic source of bromine, especially in polar protic solvents.

Here are two examples from my personal experience using the same substrate with different conditions:

Using methanol as a solvent without a radical initiator, I got electrophilic bromination of the arene.



Using 1,2-dichloroethane as a solvent with heat and a radical initiator, I got radical bromination of the benzyl position and electrophilic bromination of the arene. 



Using 1,2-dichloroethane as a solvent with UV irradiation and a radical initiator, I got radical bromination of the benzyl position.