Good rock for a tumbler should be fairly hard (5 - 7 on the Mohs scale I think) and the entire load should be of similar hardness. The rocks should not have holes or little cavities because that can carry grit from an earlier stage to a later stage where it will ruin the finish. A typical setup is to use coarse grit for a week, then fine grit, then prepolish, then polish. But there are many variants on this scheme. Look around for some rock tumbling faqs - they’re out there.
I did tons 
of rock when my kids were small. I had a Lortone sp? tumbler with a rubber barrel. 3 pounder I beleive. You start with a coarse grit which I always left for a month. by that time the grit was effectively a medium size. Then you empty the barrel being very carefull to clean all the old grit off and recharge with the next finer grade of grit. Keep doing that until you get to the polishing powder, Aluminum Oxide i think and do that for a week or two. As I recall I did 4 steps over 2 or three months. My rocks came out looking like glass. I recommend you buy some agates for the wow factor. very very nice. Have fun.
I got a kit from these guys, we love it. It has rubber chambers, is very quiet (about like an electric toothbrush) and easy to use. Their kit comes with all of the polishing stage grits. We got the two barrel model so we could run different batches at different stages. The only thing that sucks is the patience required to let it tumble and do its thing.