Worry about the rack later when you understand how a rack works and what you want from one. I go to a gym to do squats, chin-ups and lat pulls and do everything else at home with a bar and plates I bought off craigslist for $75. Being able to use the racks at the gym I can see what kinds of racks I like and what kinds I don't like. Were I to buy one now, I'd know which ones to avoid.
As a weak middle-aged lady I was able to squat the empty bar--45lbs--my first day. You are doing yourself a disservice being so cautious. You probably squat more lifting your grocery bags and laundry off the floor. Doing squats with dumbbells by your ears will quickly cease to work to build strength in your lower body because you will be limited by how much you can clean and hold next to your ears. It will be far far less than what you can lift out of a rack. I can barely goblet squat 45lbs because I can't hold onto it for long. But I can barbell squat 180lbs.
Yesterday I saw they sold dumbbells at CVS pharmacy. I believe they were measured in ounces. They had bottles of vitamins and cans of refried beans that weighed more. You are seriously cheating yourself out of your own potential if this is the way you are approaching your training.
I really loved that book, there are lots of great things about it. The father of the brothers is one of the great fuck-ups in literature. Just need a good translation, time to read, and the mind-set.