We set our budget by opening excel and making a list of what we would spend if we weren't thinking about it, then refining from there. For me, it helped to start with shopping trips instead of planned items - like "how many times do I usually go to target before Christmas? What do I usually spend each trip?" Then I made a separate list of individual items like "plan to buy the kid three outfits, two books, one big toy, three small toys, some stocking things - estimated cost for each." Comparing both lists helped refine - I know that if I go to Target I'm spending $25+, so if I go three times before Christmas, my budget shouldn't be $30 for décor/wrap/small gifts. Looking at it both ways helped me be honest with myself about realistic vs. ideal spending.
This year the Christmas budget was $450 and we ended up spending $434 - that covered 9 adults, three friend kids, our own kid, our tree, wreath and extra food and treats. A lot of stuff was picked up on a really good sale, and some things were even used. Our gift budget for adults was a target $13, although some got more than that.
If I were in your shoes, with older kids with more expensive needs (and the same age, so no hand-me-downs), I would try to go simple and frugal on the fun stuff and be generous with more needed items, like the car you mentioned. In some places a car would not be a need, but where I live it is so I relate to that.
