Within star systems, messages travel by radio and laser for relatively low cost — an interplanetary signal costs one credit per minute. Hard-copy mail moves as freight aboard fast shuttles at a price of around 1d6 x 10 credits per page.
Interstellar messages either go as mail aboard starships at the subsidized Imperial Mail rate of 2 credits for a first-class letter, or are transmitted by radio through Hyperspace. A Hyperspace broadcast goes fast — a million times the speed of light — but has limited range. In practice a radio signal can travel for about half a light-day (roughly 1,400 light-years) in Hyperspace until it degrades to the point where the receiver cannot understand it. Thus, governments such as the Terran Empire establish Hyperspace relay networks (HRNs) of unmanned beacons which receive and re-broadcast signals to maintain their coherence. (Important communication nodes often have manned communications stations as well.) HRNs are vulnerable; invaders and enemy spies often target them to disrupt communications.
Given the limitations of Hyperspace relay, a message typically travels at the rate of about 7,000 light-years per standard day on the military HRNs, or 5,000 light-years per day on civilian networks. It takes a message from Earth about a week to reach an outpost on the border of the Ackalian Neutral Zone, so the Empire picks and chooses its military and diplomatic command personnel carefully to ensure they can operate independently... but still in the best interests of the Empire.
Of course, some distant worlds, such as newly-established colonies, don't necessarily have a local HRN established to tie into the Empire's overall network. Those worlds can only communicate with the rest of the Galaxy by sending recorded messages back and forth in starships to the nearest communications node.
It costs 2 credits per minute times the number of beacons the message passes through to send a message on the civilian HRNs. Since the Terran Empire is about 45,000 light-years wide at its widest point, the most it could cost to send a message across Imperial space is 64 credits per minute.
Tapping into a civilian HRN is difficult, but not impossible — a character needs the proper equipment and must succeed with a Systems Operation (Communications Systems) roll at -3. However, finding the data he's looking for amid the flood of comm traffic is another matter entirely; that usually requires a lot of time and more rolls. Tapping into the heavily-encrypted military HRNs is impossible... or at least, no one has yet succeeded and lived to tell about it.