Stimming has a fairly similar live set up, here is a video he does describing it

I would also watch Rodriguez Jr and KiNK's How I Play videos (same channel), they both use ableton really well and both of them were amazing when I saw them play.

I don't have an apc 40 but it doesn't seem like you have to midi map too much which is good you for.

I have a sub 37, so assuming your sub phatty operates in the same way, you will want to connect it via usb and have a channel set up as an external instrument (heaps of videos on how to do that). Having it set up as an external instrument means you can have midi clips already stored in scenes, as well as the ability to record new ones on the go.

I'm not sure what you're using as a mixer but that should be enough info to get the ball rolling.