In my very early forts, I of course just have crafts all in the same stockpiles (sometimes in an "everything" stockpile that I use to get all initial embark goods off the wagon, and then later use to gauge whether I've forgotten to make enough specific stockpiles[1]) and all kinds of different ones in the same bins (if I have bins at that stage), but I'm not fussy.
Later on, I set up a nice set of stockpiles each dedicated
solely to one each of the crafts, large gems, whatever else I'm currently producing or going to trade for, and remove them from the allowable items in the 'all stuff' stockpile. The bins don't say "amulet bin" (although I think I'd love to suggest that it do, as long as it's
just amulets...) so if I want to trade amulets, I can search for "amulets", and I often have enough loose stuff (or already at the depot) to make that worthwhile, albeit it's a one-item-at-the-time inefficiency, but I can search for "bin", examine each contents and choose those... A little micro-managey, but this
is DF...
So, the same with barrels.
Also, w.r.t the value issue, when you examine the barrel and see the contents, the value displayed above that
just refer to the barrel. Dive further into the object-examination process and you can (one content at a time) find the values of the meals.
You get the same effect by viewing bins (yours or theirs) in the Trading screen.
[1] I keep meaning to use the features I know exist within DFHack (but as yet never used) to make a Stockpile Manager, a.k.a. "Things Therapist"... Probably just in read-only mode, but it could tell me if I've got redundant or uninclusive sets of stockpile acceptance set up.