Just looking for a little direction.
How often do you ski? Do you live near a ski store? I live in northern VA and outfitted my kids with a lot of used gear bought at preseason "swaps" held at or near local ski stores (these are consignment sales/yardsale/parking lot type thing, usually with a cut going to a charity). If your child is just going to do one ski vacation/week per year I'd say continue renting, especially if the vacation involves flying. But if he's skiing ~5 or more days split among several different locations including local resorts and distant ones, then buying starts to make sense for cost reasons and also to elimniate waiting in equipment rental lines before each outing. Some ski shops have children's ski equipment sales programs where you purchase new gear from year to year and get good discounts when you trade in the old stuff to resize your child (this is apart from the swap concept).
I've been guilty of buying my four kids (now mostly grown-up) crummy or ill fitting used gear. It worked, but probably slowed their development a bit. But when purchased at swaps used skis and boots can be at prices that you recoup in about three days of rental fees. For me it was the way to go for budgetary reasons, but also because for many years I never knew if they'd ski 2 or 12 days per season - depending on school schedules and local snow conditions. I also had the economies of the hand-me-down process.