I think that seems like a good intro to Critique of the Gotha Programme. I would suggest works like Principles of Communism and Socialism: Utopian and Scientific before it, if it isn't too late to change, as these both help explain what Marx is getting at in Critique of the Gotha Programme and might help the reader make more sense of it. Critique of the Gotha Programme is short, but because of its short length it also relies on the reader being more familiar with Marx's theories and methods.

That all being said, you should be fine with that intro, based on a short skim!

I also wrote a basic Marxist-Leninist study guide, so feel free to check that for anything of value to you and your group!

Tbh, imo the only context one rly needs is what the SDP was (a socialist party), and that Marx was specifically asked by someone in it (Liebknecht iirc) to criticise the programmes reformist tendencies. It could also be beneficial to give folks a copy of the programme, its not very long.

Here's a podcast about the critique of the Gotha program by Red Menace.

Edit: here's another link, because I'm not sure the first one works

In my reading group, I try to keep everyone involved, by giving them time to express their thoughts. And asking what they got from the section, if they don't speak up themselves. Since I have more experience with Marxism, I tend to want to talk constantly and info dump more than people can process, so I have to actively remind myself to shut up and stand back a lot and let questions come up naturally and even then I try to let others answer first. My goal is to radicalize as many people as I can and so far, some have already asked me for more Marxist reading material on the side.