I'd definitely recommend barrels or trash cans for cobble, gravel, and dirt. After that, depending on how well your ore processing is set up, you could either run the rest into an enderchest that feeds your ore processing, or you could just stick an obsidian chest after the barrels. You may have to return every so often to empty some items out and take them back. If you're playing with Blood Magic, you could use teleposers and a timer to periodically swap your quarry chest with your chest at the base, but that's probably more effort than its worth