"Does the modem plug into the router?"
Yes, if you're a cable customer, but you are an ADSL customer, so the modem goes.
And in its place; a modem/router, such as the Belkin 7632 click here (my pref over the updated 7633 for its USB printer port).
"Is there a monthly charge?"
And are you sure that you can justify the extra expense (not much, admittedly) of a propreitary boosted system? Are you planning to stream large files such as multimedia content across the wireless part of the network? If not, I suggest you settle for a standard 802.11g router and leave the "pre-n" stuff for now.