Which Bra during Radiation

I am starting on Wednesday and to be honest, I am thinking of wearing a soft loose singlet under my long sleeve tops (long sleeve to stop the sun - and loose).  That is if I am going out.  Same under dresses and big/comfy T-shirts.  Maybe get a couple of black and white ones, maybe with a bit of soft lace pattern at the neck?  I had a total axillary clearance in my right arm after my lumpectomy and found the best bras for me were the Chloe and Lola maternity brands in Myer.  No underwire. They were expensive but the one I bought at Target irritated my axillary scar.  When I am at home I will be going bra less.  I'm the sort of person who takes off her bra when she gets home!  I think I will use my old nighties at night as I intend to slather myself with cream.  I'm also planning on using one set of sheets and pillow cases and washing them weekly so my Calendula Cream doesn't put oil spots on all my nice linen.  I was told to wear loose clothing, nothing tight, and natural materials like cotton are best.  I haven't read anything to date about needing to wear a bra during rad ... if there is a reason to, please let me know!  Good luck for your rad xxx