Quick and easy would be something based in Ableton Live triggered by scenes and simple settings.
You're looking to play sax over what you generate. That's an instrument that you really can't play with one hand and tweak settings with another. Everything in Eurorack must be patched and tweaked and might need lots of meddling with. How many bars and beats can you hold off playing your axe while you twiddle with Eurorack?
If you were already experienced with Eurorack, you might be able to pull it off. But if you're new to the platform, you're asking a lot of yourself.
Okay with that said, I'd look at the Tip Top Trigger Riot, a Euclidean capable module, as well as a Turing Machine module. I think Pam's New Workout can do Euclidean, but don't quote me.
The Monsoon is nice. But it's one of those modules that takes a lot of time to hit the "sweet spot" with and there's a lot of unlabeled modes and features. I wouldn't bother with it if getting to a sound quickly is where you're at. I'd replace it with a reverb module and multi-fx module that can do flanging, comb filtering (if possible), and possibly a phaser.
One thing that's missing is a performance mixer. You need to be able to manage all of your audio sources quickly, including effects. I don't see that here.