When I was growing up, we had stocking plus "parent" presents from Santa, all opened first thing. Presents from other relatives given when we saw them around Christmas from the relevant person (and put under the tree until Chrismas day if we saw them beforehand).
In DH's family, they had a small stocking from Santa and some presents under the tree from Santa and some from parents (and other relatives). Stocking opened first thing and tree presents after lunch.
We ended up doing a bit of a combination, recognising we would spend some Christmases with each side of the family (involved staying over given distance, and sometimes with other family children also staying over so approach needed to be similar).
So we did a large stocking from Santa (including some "proper" presents from the list) opened first thing. Main present (or up to about 3 presents in a year where there was no one big thing) from us under the tree, plus a couple more presents from Santa under the tree (generally things like family games or a book collection). Tree presents to be opened after lunch, but in years when at my parents' house they were also allowed to open the tree presents from Santa first thing if they wanted (in line with their cousins).
We slightly shifted the balance between parent presents and santa presents each year depending on where we were and they never particularly noticed.
They always enjoyed having to wait until after lunch for some of their presents to keep the anticipation going - i was worried they would struggle with this .
The are now teens and we still do a mix of stocking presents first thing (reduced in number but not value!) and main presents after lunch.