industrial connectors are colored by the highest voltage present
in single phase conenctors this is the voltage between the live and nutral so britsh mains single phase wired between a phase and nutral is blue
3 phase conenctors for british mains are red as are single phase conenctors for intended to be wired phase-phase (never seen theese used in practive but they are made)
single phase connectors are refered to as 2P+E
3 phase with no nutral is refered to as 3P+E
3 phase with nutral is refered to as 3P+N+E
all are availible in current ratings up to 125A
probablly the best connector for your perposes is a 32A blue 2P+E the supply to this should be wired on a dedicated cuircuit with a rating to match the socket (as you would a cooker or shower cuircuit)
another alternative is the 20A powercon but you would have to put this on a wallplate yourself and you aren't supposed to use them in domestic installs because you can dismantle the plugs without tools
as for the flex to the device if it's on a 32A plug you should probablly use 4mm flex if you go for the powercon you want 2.5mm flex these are availible
here
a 20A powercon would only need 2.5mm flex
within the device the motors should definately be fused seperately i dunno whether you want the motors switching seperately or not if you do you could use a 6 way grid plus box with 3 switches 3 fuses (and the switches after the fuses and mathed to the fuses that is 20A switches with 13A fuses)
if you want them all controled from one switch a small din rail cu is probablly your best bet
what exactly is this device supposed to do?!