AR+MC means Action Replay and Memory Card (Official Nintendo). Dont use 3rd party ones.
With GCOS (Gamecube Operating System) you dont need a modchip to play backups. You copy the Gcos files to the memory card via the BB adapter. Then use the AR to boot the files from the MC in Slot 2. Choose Game backup and swap the AR disc for your Backup when prompted. At the moment Gcos is at version 1.4 using Cobra bios 0.4. Cobra have just released 1.1. and Gcos 1.5 and possible 1.6 is in the works.
goto
www.maxconsole.com and check the forums there, as there is loads of info.
Mods it's okay to post a link to this site?