I have a small home office that is in the farther part of the house, no one bothers me. However, I cannot study in complete silence nor while totally alone. I would put my head phones in, listen to the recorded lectures and read my notes in the living room where my family would be watching TV or chatting or whatever.
When it got too loud, I'd leave that room and go into another room close by but far enough away to still hear the normal day to day noise of the house.
Must haves for me: light (not overly bright but bright enough to read), somewhere comfy to stretch out, a place to lay my book(s) out an a place to put my coffee .
We have a sectional couch with is rather large so I was able to stretch out and put my book out and the family could still sit comfortably on the couch with me.
But thats just me, others I know need 100% silence and to be totally alone while studying.
My husband built me a unique desk to fit the corner of our bedroom so I could be away from my family's noise. But the one must-have that helped me keep my sanity was that I bought a 10 gallon tank, put a beautiful & funny Betta in it, & put it in the corner of my desk. You would be surprised how being able to look over at that pretty tank every once in a while helped tremendously.