When I was growing up we had stockings (actually a pair of tights with a knot on one side - apparently when I was about 2 I was in floods of tears that Santa would think that as I'd put out my dad's rugby sock that I was a boy, would not be convinced that santa would know I was a girl. Parents used pair of red tights for each of us, knot on one side and my sis and I used them until we were in our 30s
).
I've carried this on with my dc - stocking in the morning when they wake up, they still come and wake us up to do it, haven't started to do it themselves. Always has satsuma at the bottom, along with a bag of chocolate coins, a vest, new pair of pants and socks to wear on the day, maybe a nice tshirt too if there is space. There's usually a couple of toy cars, a comic they like (gives them something to do if they have woken up early and dh and I are able to doze a little longer 
, maybe a playmobil person or small set, lego often do small christmas sets for £3 that are in bags and ideal for stockings, a new toothbrush, a small pack of crayons/colouring pens/pencils, a small colouring book or notebook and maybe a small card game or something similar. If I have any left over bits from party bags (bouncy ball, soldier with parachute etc then I'll pop them in too. (can you tell I've got boys!). Means they have presents to open, chocolate to eat first thing, and things to do and play with so dh and i can lie in so we can have a gentle morning. DS1 got given a gorgeous handmade stocking for his first christmas by my godmother, which he uses. I was hoping that ds2 would have got the same but he didn't so had a mad panic to buy one for him just before his first christmas (and failed so had to use a santa's hat!) - he now has one but it's not as nice as ds1's.
Then we go downstairs, have breakfast, get it cleared away and check on how turkey is cooking etc, and once we are all set, the dc are finally allowed into the lounge where most of their presents are under the tree. Main present is usually hidden at the back so it is the last opened - often after christmas lunch if we can stretch it out that long, means that there is something to look forward to after lunch - and to use as a bribe for good behaviour! I am also really rigorous about writing down who gives what present to which child - dh has loads of siblings, most of whom now have grown up children so they like an excuse to get back to the toyshop to buy toys for younger kids it seems!
Dsis on the other hand was manipulated into following her dh's family traditions and she really doesn't like it. The kids have massive stockings (all made by her MIL, who loves sewing things but makes them up from kits rather than actually creating things herself - but made them without asking and showed them to the eldest kid as soon as she was old enough to see and told her all about xmas morning so it was a done deal 
). These hold pretty much all their presents - so as soon as her kids wake up they want to go downstairs to open their presents, in their pj's and dressing gowns. Everything is in them, very little is under the tree (what is there is mostly from other people) so they race through their stockings, ripping everything open as fast as they can. They've also been known to start and go through things quickly encouraged by their dad (ie bil) as he needs to get out to sort out the animals on the farm and he doesn't want to miss out - but he's quite happy for dsis to miss out because she needs to do stuff for breakfast or lunch 
. I digress. sorry.
Anyhow, they don't seem to appreciate the quantity of presents they have or what they have - it's more an exercise in getting through it as fast as possible, then move onto the presents under the tree without looking at who has given them what. then dsis is making lunch and the kids are just left having a normal morning and all the anticipation of the day has gone.
So having seen two different ways of doing it - definite vote for sensible sized stockings first thing that can be done upstairs before breakfast and then having presents downstairs later on after breakfast!