Having supply ships be mostly player-controlled seems to me to be a bit convoluted and not very fun. I think that it should be almost completely AI controlled with the player only making a few major decisions.
Let's say you have a big fleet. All planets will put forward an equal % of their resources to supplying that fleet. The %, of course, depends on fleet size, # of colonies, and tech. A special building can be built that increases the amount of supplies that come from that planet, thus lowering the % of resources used by all colonies to supply ships. This building would also instantly resupply any friendly ship in the system in which it is built. (It seems illogical to me for millions of kilotons of fuel to be instantly generated when a fleet stops at just any old friendly system.) These, like most buildings, would be fairly expensive and specialized so that they would only be built for in special strategic positions.
Ships can only be supplied if they are within a certain number of star lanes from the nearest colony. Not entirely realistic in a very large empire, but the simplest and most fun for the player IMHO. This number of star lanes would, of course, increase with technology.
Now for the important parts that the player can control if he wants to:
Maximum % of resources to put towards ship supplies.
Which planets will contribute and which will not. (A simple toggle.)
Which ships to give priority to in case of a supply shortage. (Again, a simple toggle. The AI will give supplies to the ships closest to enemy territory as a secondary priority after the player determined top priority ships have been supplied.)
Where to build the important supply generation facilities.
Ships, naturally, ought to require fuel based on their size and the distance they traveled. Considering the immense difference between traveling to a different star system and traveling within a star system, I don't think battles should require any fuel. Moving from point A to point B on the battle map isn't even a drop in the bucket compared to point A to point B on the star map.
There are four small things for the player to decide and everything else about the system is easily understandable, so the player shouldn't be wondering "Why is that ship moving at less than 1 parsec per turn?" when it runs out of fuel. Since supplies are really a minor part of the game, the player really won't want to get too involved in them. This solution simple and efficient.