I'm finding the 2-stockpile method up near the farms to be the best with the new system. But I basically run a 4-tier system. All of the stockpiles which accept plants in barrels are setup to "only accept from links".
(farm) -> (no barrel stockpile) -> (uses barrels stockpile) -> (main stockpile in middle of fort) -> (supplemental special purpose stockpiles) -> (workshop)
So, if I have a bunch of 3-6 tile farms, I will create a small stockpile near those farms which accept only those plants types and which disallow barrels. If the total farmed area is 50 tiles, my next-door no-barrels gathering stockpile will be about 10-15 tiles. Next to that is a small 10-15 tile stockpile that takes barrels, the same plant types, and which pulls from the first stockpile. Next to that is a small 5 tile stockpile which accepts empty barrels (furniture, barrels & large pots).
Then I have a larger 5x10 up to 10x15 stockpile deeper in the fort that uses barrels, accepts all plant types, and which pulls from any farm-fed stockpiles. It may also have a small-ish stockpile nearby that accepts all plant types, but takes no barrels, which also feeds this main stockpile.
The reason I use a "main" stockpile is so that I have a convenient location to draw specific plants off for specialized industry. Since we can't (yet) name our stockpiles, you have to place in-game notes or just remember that "this is my main stockpile of plants". For food, plant and drink distribution I will setup (3) largish (5x10 up to 10x15) stockpiles in the middle of the food-prep and then pull from that to the rest of the fort. One stockpile accepts all plants, one accepts all drinks, and the third only accepts prepared meals (stockpile, food, turn off everything, hit 'u' to allow prepared food, set the stockpile to maximum barrels).
Then I setup a small 3x3 or 5x5 area by the still which pulls plants of the proper types, in barrels from the main stockpile. I'll also setup a 3x3 up to 5x5 area by the still which accepts barrels/pots. Both of those give to the still.
I try to avoid situations where I have longer "give/take" chains. Out past about 6 chained stockpiles and I have trouble remembering what pulls from what and why. So I try to classify the stockpiles into "gathering/source/inputs" (which feed the "main"), "main", and "end-use" (which feed workshops).