What size junction box do I need?
Given the large size of the conductors, I would use aluminum for this, specifically the new AA-8000 series alloys.  Yes, aluminum has a bad reputation as a wire. But that only applied to the faulty AA-1300 alloys installed during the postwar housing boom, and even then to the small-gauge stuff where it was used instead of 12-14 gauge copper.  1300 is now outlawed in any gauge. 8000 is fine, and about 1/3 the cost of copper.  The wire-run chart says to use 2ga aluminum. Which will require larger conduit.  

Second, it sounds like you also want 120V convenience outlets out there too.  But if you didn't need that, I would ask your vendor if they offer a machine that is 240V instead of 120V, and wire a 240V 10A circuit.  That would let you do this in 10ga copper.  (In those smaller sizes, aluminum isn't much cheaper.) 

Double the voltage, halve the current, quarter the losses.