If you're going to rent a mini excavator for stump pulling, try it at a "tugging" task before you accept it for the job. I've owned a John Deere 15 (quite small) for 25 years. A few years ago, a friend wanted me to take it to his house, 75 miles away to pull some stumps, and move some rocks. I told him I was entirely happy to help, but that it would probably cost less effort to arrange for a delivered local rental, rather than arranging truck and trailer to move mine all that way. He agreed, and rented a rather larger one. I went to do the work for him, and it was gutless. Mine would have easily done the work. Though a bigger machine, I saw that the hydraulic cylinders were smaller, and I don't think it was really built to work, but rather play. And, I wonder if the rental agency had dialed back the hydraulic pressure, so the machine could not be worked hard. I don't know how you judge the suitability of the rental machine before hand, but I know that too weak a machine is a waste of your day....
As for learning, just make sure that there's nothing close by you can hit by accident (swinging), and go slow for the first few minutes. Don't use the swing to move rocks sideways, lock the cab to the tracks, put the blade down, and use the boom swing instead of cab swing. And work over the blade as much as you can.