Don’t forget that the ships exist to achieve goals. Constructive and destructive interactions with facilities. There was supposed to be a siege capital to attack surface installations, right? So the Cruiser would have some kind of heavy weapon intended for that. That same weapon could be used to nail another capital, just like EVE Online’s Titan weapons. They take a while to activate, but when they fire, they hit hard.
I bring that up because it can change the modality of the Cruiser. If the Cruiser is working on firing its siege gun, the rest of its systems may be heavily compromised, requiring lots of support from other ships to keep it safe. When not playing siege engine, it could be a straight-up capital brawler.
Please stay far away from labels like that, especially so early in the design process. As soon as people start thinking in those terms, it’ll be all over for Battlescape’s gameplay. It will BE DPS/Healer/Tank, and all players who have played that trio in other games will instantly recognize it and dismiss Battlescape as “World of Warcraft in Space”.
That said, @Sab1e’s basic list does exclude support roles. Ammunition and repairs are certainly necessary supplies. Carriers are essentially a support ship and may be the ideal way to have a kind of forward operating base. They can carry supplies, ships, and perform repairs. Flavien has stated that Carriers will act as spawn points, but I’d argue strongly against that - unless a carrier has a limited total number of respawns before it must return to base to restock. If a carrier can carry 20 interceptors and 10 bombers, then that’s the number of times that players can respawn at that carrier before it has to go visit the interceptor factory to get 20 more interceptors and the bomber factory to get 10 bombers.
The Destroyer should also be capable of being configured for logistical support, but the Cruiser should probably be impractical as a logistics ship. It could be done, but the return on investment just wouldn’t be there. Why? So that the Carrier remains the king of logistics. The Destroyer would be the lighter logistics ship.
For supply transfer and repairs, please don’t put in magic beams. Just hard dock the ships and do what needs doing. Put particle effects all over the damaged ship while it’s being repaired (welding, grinding, sloppy laser sintering, whatever). Supply transfers would be through the dock point, so there’s nothing visible there.