Are you asking about a router or a modem (or a combo device)?
The modem takes the data on coax line and outputs it as Ethernet.
The router takes that 1 connection and turns it into multiple connections for multiple computers.
To avoid paying any monthly charges you will need both a router and a modem.
You will not find a combo modem/router for $40 or less, and even the $100 combo devices are not good.
For a cheap but good router look at the netgear wnr3500l, or for a small step up you can get a tp-link wdr3600.
For a modem I cant give you a good recommendation for your price range. I have time warner but had to replace modem not long ago. Since the Comcast/TWC merger has yet to be approved or rejected I had to look at what modems...