Headset hands down. You really don't need much of a connection to play COD games, it's based on a 1999 game engine so any modem will be fine. Besides, it is your opponents crap connection that messes you up. Being able to hear footsteps and their direction is a great advantage to have and IW, who makes Ghost has had great footstep sounds previously.
Normally, an ISP provides a modem. Are you sure you don't mean router? If you do the answer could change depending on your other uses for the connection, but from a strictly COD perspective, I would still go directional headset. Being able to communicate with team mates is another big plus when gaming.
Like Kothar44 said, you do not need modem/routers that do QoS, bandwidth shaping etc...
A good headset is an absolute must. Any headset (dual ear, not a bluetooth earpiece) is better than nothing (TV speakers, even a surround stereo).
A good headset will provide you with directionally of the sounds you hear, on a vertical as well as horizontal plane.