[Psitticine]

If you group ships into a fleet, their supplies are pooled and divided evenly between ships at the end of the turn (or maybe at the beginning of the next turn - I can't recall right now.)

I think it'd be nice to have a Shares Supply With All Ships In Sector option for a fleet so you wouldn't have to do that - just move the fleet into place and let the transfer be automated. It'd be especially nice when you are, like me, using warp point stations for refuelling.

As for what to use in a supply ship, well,it depends a lot on your tech. Supply modules are nice for basics. Emergency supply pods are also useful. Solar collectors are a personal favorite, and the almighty Quantum Reactor can solve all your supply problems for good.

I usually have a support ship flying in the same fleet as my combat ships. It'll have repair bays, extra supply capacity and/or solar collectors, and possibly an emergency pod or two. In combat, it wisely pulls back out of the way so I don't need to group/ungroup it continuously as the battles rage.