I always took DD shopping but from a very early age got her involved in the shopping so where is the x where is the y, when toddling she fetched things I pointed at and when a bit bigger did herself now at 10 I can say can you get bread and she gets the best deal bread, and if there is something else she thinks I wld buy if on offer will tell me and hare off to get it if I say OK. I have been laid up with a bad back/leg and barely walking for about 6 weeks and it was a godsend - I just pushed the trolley down the middle and she did all the shopping!!!
Also teach them simple meals they can do themselves so something on toast, sandwich with child knife/normal table knife) baked potato (we just progressed to using oven) she can also do cakes and is now progressing to pancakes.
As a baby we used the Muslin for top of moses basket matress trick, Also used cartons of baby milk overnight with a flask of hot water upstairs. I also minimised her nappy bag to a small childs rucksack that just hooked on the back of the buggy and never tipped it - mini cream pots small pack of wipes which I used to refill or use a sealed sandwich bag to store small amount, one or two nappies and a clean vest and a small thin change mat that folded up small. I cld also squeeze a carton of milk or pouch of food in.
We also had two great products from fleece - one was a baby pocket with feet and wrap top - dead easy to get her in and cosy, second was when she was a bit bigger was a poncho with sewn arms and a hood again quick and easy and warm.