We rent boards and boots for the season (helmet we just use his skate helmet that gets used for everything; bikes, skating, snowboarding, etc. Helmets fit for years and buying a good one is just soooo worth it.) Not a big fan of waiting in line for daily rentals, I like boots on at the car, and the lifts start up before the rental shop opens (riddle me THAT?).
But it really depends on how often you're going. Here, a season rental is only about 150 (full kit) and daily rental is 40. If you're going up 4 times, a season (nov-apr) is worth it (we're up 3x-5x a week). If NOT, then it's a Q of whether not standing in line is worth the extra cash. NO IDEA what daily and season rentals are in your area.
As far as boots and boards or skis go... they outgrow those FAST. We've even had to switch sizes midseason (where we rent, we can change up).
In our area there are a LOT of ski and snowboard "swaps"... where parents bring their kids' used clothes and equipment to sell for rock bottom prices and to buy "new" (aka someone else's used) gear for rock bottom prices. Round here, though, that usually happens in October.
Clothingwise... we spend a lot (I always seem to miss the swaps!!! Someone has the stomach flu, or I'm behind on a paper). The wateproofing on kid gear is practically nonexistant (:P) and that can make or break a day. So we tekwash on our gear all the time (instead of regular detergent; to help maintain the waterproofing and breathability), AND rewaterproof it fairly regularly. As far as brands? Burton, O.R., Northface. None cheap. All great.