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You want to pick up the cleanest brass possible (though it isn't terribly important), but the main issues when picking up brass is collecting the correct caliber, making sure the brass is in good shape (literally), and it hasn't been reloaded too many times. Most rifle casings work just fine together. Common pistol calibers are a bit more picky as casings will wedge themselves in the openings of other larger caliber casings. .45s and 9mm work just fine with each other, but adding .40s into the mix will create problems. When cleaning .45s, .44 Magnums, .40s, 9mm, .357 Magnums, and 38 Specials all at the same time, clean the .45s, .44 Magnums, and 9mm in one batch, and the .40s, .357 Magnums, and 38 Specials in a separate one. You can test to see if casings work well together by trying to fit one casing into another, if it is even remotely tight it won't work. The easiest way is to use a vibratory case cleaner. The case cleaner uses a media to clean the case, and optionally you can use a polishing additive to make the casings look almost as good as new!  The media is usually ground corn cob or walnut hull, but liquid media is also available. The media is what makes the tight fitting cases stick in each other. When the media is not able to cycle (because it is jammed in a casing) it cannot clean as well. Note that the media is reusable, and less polish is needed every time you use the same media. Depending on how dirty the brass is, one batch of media may last anywhere between three and eight cleanings. This allows for easy access when loading so you don't have to pick up handfuls of random casings to find the one you want. It will speed up the process in the long run. Usually you place each different caliber into separate bags for transporting or storage.
Pick up empty casings from where you shoot or from a gun range which allows you to collect brass. Sort the casings, the level of sorting (before cleaning) depends on the calibers being used. Clean the casings. Sort the casings into separate calibers.