A cheap random orbit waxer doesn't do much more than you can do by hand. But I still use one. You will only use it to apply the wax. Thinly. You still buff it off by hand. Make sure the car is CLEAN. You don't want to random-orbit a piece of something all over like tar or a stone and scratch your finish.
So yeah, Wash, dry, wax. Polish would come between the dry and wax, but I thought you were using a one step product (like a cleaner wax).
Others here will run circles around me, so if in doubt listen to them. The fact I can do a good enough job to give advice is a testament to how easy it is, not how good I am with a buffer.