For just the basics I'd do a cheap Zoom multi, I have the B1 Four X on a little board with a Joyo Sansamp clone, that covers me for quick and dirty covers and rock stuff. My main board has a Stomp XL, which in future I'm planning to swap to an Anagram when I've got the money.
As for how you manage big, complex boards live, it's usually a MIDI controller. More and more pedals have some form of MIDI control nowadays, which allows a user to program a foot controller to switch pedals on and off, change presets, etc. all with one footswitch. Prior to my current board, I was running a Source Audio Aftershock and a Line 6 M5 as well, along with some other non-MIDI pedals (Pitchfork and a couple of others). I used a loop switcher that was MIDI enabled to control it all, switching sounds with a single press of a switch when I needed to. Great live, but the caveat is that you need to spend quite a bit of time setting up your sounds beforehand.