I would suggest buying a set of rocks to tumble first, so that you can follow the process and get some good results.

Lots of rocks won't tumble very well and it can be disappointing to find that out after weeks of tumbling. So I always suggest buying rocks that are known to be good for tumbling for your first time, so you can see how the process works and what the results should look like. After that you can experiment with different rocks and see how they tumble and compare against the first batch.

As OP said, you'll need to tumble rocks of similar hardness, otherwise you may grind a rock to nothing.