I'm gonna have to actually set up the same thing over here to give you definitive answers. I do have a 4k though, a little short on table space right now, and it's like 1AM over here.
But here's the walk through on the Akai site, should be some help. Although it's for the newer MPC's. Shouldn't differ too much if at all though.
http://www.akaipro.com/syncabletonMMC would be MIDI Machine control, used for having the transport controls work in tandem.
You mentioning that you want Ableton to start/stop the MPC means you're going to want the MIDI master to be Ableton as far as looking at the instructions at the Akai site.
Control Surfaces is for supported MIDI controllers that Live has built in scripts for, allowing you to not have to really map anything manually. More for MPD's, MPK controllers and other MIDI controllers or MIDI mixing surfaces like a BCF 2000 with it's knobs and faders. So you probably will skip that. The input/output would set to on with the BCF 2000 for example so if I move the fader on the screen the motorized fader moves too or vice versa. But again, that isn't needed here.
You'll be looking to have the whatever your MIDI interface is called in Ableton as where you'll set up the 4k's MIDI.
That's in the MIDI Ports settings under the Control Surfaces section in Live's preferences. I think you'll want to activate Track on both the Input and Output listings for your USB to MIDI interface, whatever it's called in the list. And also enable the Sync tabs.
The Remote tab is for Live receiving MIDI from an external source/controller like if you wanted to map something to control Live's faders or knobs. (The Remote mapping mode is engaged by hitting the box that says MIDI in upper right corner on the Ableton GUI, next to the CPU meter)
Pretty sure you can set the Q-links to send out MIDI CC #'s to Live to use the Remote mode.
Like a lot of what I post here I do it from memory, and when it gets more specific I need to actually get it running myself to give clearer answers.
But see how far you can get off the Akai instructions. And even if it's tomorrow I will post again after I have tried this setup myself. I've never used my 4k with Live, only a 1000 and 2500. Also someone more knowledgeable than me might post in the between time. I haven't made too much music this year. Any I have has just been with MIDI controllers and a mouse lately.