As a child, we had pillowcases (just a random clean one out of the linen closet) which we put at the end of the bed and would wake up to find Father Christmas had been.
It was very exciting when you finally woke up to see the bulging presents - they were mainly small silly type toys, with a couple of practical things like pants, a selection box and always a satsuma.
Father Christmas also brought a selection of random gifts under the tree (a couple of 'family gifts' such as a new board game, big keyboard or something else). All the other presents just came from mum & dad or relatives - so we could knew who gave them and could write thank-you cards).
My mum would also put the presents out bit by bit, so the pile slowly grew, then most were added on Christmas Eve.
With our DD1 (4) we got her a nice red sack (an upgraded version of the pillowcase), which we get her to leave by the fireplace with a snack for santa/rudolph. I do like to put slightly better presents in that will actually get used, craft stuff, stickers, puzzles aswell as a few cheapy gimmicky things and some sweets (the sack is easier to fill than a stocking). DD2 is a baby and will get a "babys 1st christmas" small stocking this year and for next year I will need to find a similar red sack for her or get them something the same.
In addition to the stocking we buy DD1 a few biggish presents for under the tree and allocate 1 or 2 from Santa (sadly not Father Christmas where we live), this year she has asked for the Elefun game from Santa so that will be from him and maybe one other thing. Her main present of Playmobil will be from us.
When they are older we will probably leave the 'stocking' presents outside their door (not brave enough to attempt end of the bed!) so they can open them together first thing, like me and my brother used to.