So I broke down and got the game. I've been using the Scott Manley tutorial videos, and they've been pretty helpful, but in my case, as they say, "you can't fix stupid".

I got into orbit on the first try using the tutorial, did the second try without the tutorial, and am doing a relatively good job of (eventually) getting the periapsis and apoapsis within 20% of each other. Then I tried his second tutorial, Minmus, and...yeah.

Got there on the third try, slammed into the planet. Slammed into it a couple more times along the way to my tenth ******** try, at which point I managed to land. I even got back safely, though I was so low on fuel that poor Jebediah XII had to orbit Kerbin four times as I used minimum-power one-second burns at optimum points to de-orbit, winding up with 0.17 units of fuel when I finally popped my last stage. But hey, he lived (for once)!

Now, on to learning how to make better rockets. As I expected, "swap the engines and fuel tanks for bigger ones" didn't help at all, but I was surprised at how little effect bolting on an extra 2-solid-booster stage had on my launch