I went to the wig library & borrowed a wig & scarf after getting my hair cut as short as I could tolerate & felt happy with the wig thinking I would wear it everywhere when my hair fell out.
Well my hair came out in clumps & I found I was just wearing the scarf or beanies that my bestie made me. I found getting ready was so much quicker & actually revelled in the fact I could just shower, pop on a scarf & go out.
The times I did wear the wig we had some very funny moments, it would have us crying with laughter instead of being mortified as I thought I would be. That's also what friends are for, to keep you from despair.
I just let my hair fall out naturally but wigs do fit better with no hair underneath. My hair has grown back curly & yes, people can't get over the curls. Some women look great without hair, I was told I looked like Uncle Fester!!! It doesn't take long to all come out & by leaving it come out naturally it wasn't such a shock. Apart from the cold I didn't mind not having hair, do what you feel most comfortable with.
Best of luck with your treatments too.