The B&W ASW608, ASW610, and ASW610XP sealed subs are part of the 600 series B&W loudspeaker line. As such, they are highly compatible with the 683s. In your relatively small room with the 683's two bass drivers (rated down to 38 hz), you may not even need a sub for music unless you really like to feel those low frequencies pound away (like I do)!! For HT, then yes you'll need a sub for those explosions and other low frequency sound effects.
For your room size, my best guess would be to go with the ASW610 with a 200W output and their new more efficient digital amp. I actually just purchased one two weeks ago as a 2nd sub in my system to balance out the bass extension and improve on room loading. But my room is 23' x 13' x 8' high with two openings out to hallways and thin carpet on a slab. A room 12' x 14' with the 683s is a different set up. That's why the 610 may be your best choice and more than you need. Just my input for you.
For your room size, my best guess would be to go with the ASW610 with a 200W output and their new more efficient digital amp. I actually just purchased one two weeks ago as a 2nd sub in my system to balance out the bass extension and improve on room loading. But my room is 23' x 13' x 8' high with two openings out to hallways and thin carpet on a slab. A room 12' x 14' with the 683s is a different set up. That's why the 610 may be your best choice and more than you need. Just my input for you.