First, tumblers do not take off tool marks - files, sandpaper and you do that job. Tumblers are to clean and polish unless you buy special media for specific jobs e.g., grit to polish rocks or, I have some ceramic media to de-burr chains, it is very aggressive. I don't use my tumbler to harden metal, I use my tools to do that, I can't imagine how long you'd have to tumble metal to get anything but the very outside layer of the metal hard.
My pieces are completely finished other than the final polish when they get tumbled, all the filing is done, no marker or firescale stains, etc... I tumble pieces for 15 - 20 minutes with stainless steel shot and burnishing compound and get a marvelous shine. I also tumble pieces for about 5 minutes the day before a show - to get the sparkle and just cleaned look.
I find that copper needs to have the tarnish removed before tossing into the tumbler. Once the tarnish has been removed, toss into the tumbler for a 15 minutes or so and it will be beautiful (at least for a day or so!). There are plenty of ways to clean tarnish off copper - I think flat Coke, vinegar...just google it - you find loads of home copper cleaning recipes.