What a great thread. My DS (10) has been playing for 4 years. Here are a few things I wish I'd known about.
There are lots of different types of boot/trainer. Astros, moulds, studs etc. Check with the club what they will need. Different surfaces require different soles. Summer dry ground is different to sodden or frozen winter ground is different to 3G etc. Certainly with my DS, it's all about having the latest boots as well. 
It can get very expensive, with growing feet and constant new trends, so we build in as Christmas and birthday presents.
Ditto any strip. We have never bothered with a full strip, rather a mismatch of socks and sometimes different shorts/tops. Long sleeve tops are important for the winter, as are base layers. Base layers are expensive but IME buy big as they can last a good few years as are stretchy. Worth buying good ones if they play a lot. DS currently has a club strip, home and away, a district strip, home and away, a club training top, and numerous other tops and shorts, plus a few pairs of socks. Check what of anything the club will provide before you go out and buy loads.
Don't tumble dry football socks as they shrink.
Get the right size shin pads.
For you : Very warm clothes, to protect against biting winds, so hat essential IMO. Also boots for you that you don't mind being covered in mud. Wellies no good unless you have thick wells socks, your feet will freeze in winter.
A really good thermos and snacks/sandwiches for child once they've finished. Lots.
If they have a younger sibling you have to take with you, is can be a challenge. We try to have it so DD doesn't have to come as she has no interest whatsoever and is therefore bored and a PITA.
But the most important tip of all : if you ever get a choice of club that she plays for, choose one with an indoor viewing area with comfy chairs and a bar/coffee shop. 
They aren't the norm, but if you find one, man is it a delight.