The single tile trash can trick in Dwarf Fortress

Turn them into rock blocks (since a lot of blocks will go into a single bin in a storage room and that's much neater). Clearing every stone takes a long time, but you can clear certain areas using burrows:

1. Designating a burrow over the area you want to clear.
2. Select a lowly mason who will be your exclusive stone block maker and assign him to the burrow.
3. Build a mason's workshop inside the burrow.
4. Use the profiles screen on the workshop to restrict the dwarves that can work there to your chosen mason. (You'll need to have a manager for this.)
5. Set make rock blocks to repeat!

Your lowly mason will dutifully go about their business selecting only stone from the burrow and will automatically take breaks to sleep and eat, so this is a pretty low-maintenance method.

I would suggest using a manager noble and the management screen (j, m) where you can queue up tasks. I find it useful to do thinks like:

• Queue 15 barrel
• Queue 15 brew drinks

And jobs that are managed are automatically re-assigned if they fail for any reason including lack of resources. So in this case the brew drinks would be re-assigned until the barrels are available to complete them.

Note that these tasks will process in parallel.