Unfortunately, there is not a Sheldon Brown. Waxing skis and tuning edges is relatively simple, so if you are interested in learning how to maintain skis you can buy a file guide, a file, a diamond stone, some wax (the cheapest ski wax is fine), and an iron (I use an old clothes iron actually) and take care of your own gear. I learned from a friend but I'm sure there are youtube videos out there.
Of the things you need (skis, boots, bindings, poles) boots are the most important. If you're budget is limited and you can only afford one nice thing, spend money on boots that are newer and fit really well, and buy older cheaper skis. Ski boots that fit you should be very snug, not slip at all, and not rub weird in any places on your foot or calf. Do not size up for comfort (as I saw many customers request when working in a rental shop) - you will not be comfortable if your feet are slipping around in your boot. Get cheap used skis/bindings to start. If you just started skiing, you may be improving fast and outgrowing short skis, and you don't really know what type of skiing you like to do and what ski shapes will work best for you, so just get used and cheap skis to start with. As you ski more or your kids get bigger and are no longer outgrowing skis every year, then you might consider demoing a few different types of skis and upgrading to nicer skis.
You do need a helmet and googles, but if you already have winter coats and pants you can wear those, no need for ski specific clothes.