I keep my used media stored in recycled Arizona Iced Tea jugs. They are one gallon in size and have a relatively large mouth which works perfect with a funnel I made from the top of a 2 liter soda bottle. One jug of walnut media is a good measure for the amount of media you will need for the large bowl of the Lyman 1200. I state large bowl, as some 1200's are sold with both a large and small bowl.
When you get an itch to try something different, go to your nearest Wally World and pick up a bag of Kytee walnut bird litter, appx $7 for 5-6 lbs. Splash 2-3 tablespoons of mineral spirits or paint thinner in there, let it tumble for 10 minutes to mix/distribute, then add your brass (always do this regardless of what media/additive you use!). Your brass WILL come out clean. Use unscented mineral spirits if the solvent odor is offensive.
Also, look at getting an appliance/light timer to govern your tumble time. Two hours is a plenty, and can easily be controlled if you have a life other than just watching a tumbler.