Don't confuse a router with a modem. A modem has one port for your provider, either RJ-11 (phone) for DSL or coaxial for cable, and one for your computer/network (RJ-45 - Ethernet). A router has an RJ-45 as an input from your modem, and RJ-45 and/or wireless antennae for your network.
The modem is specific to the type of internet service you have. The router will work with either. If you have only one wired computer, you don't need a router. You can connect your computer directly to the modem. If you have multiple computers, you need the router (or hub/switch if they're all wired).
Stick with one of the major brands sold at major retailers and you'll be fine. Picked the lowest cost, highest review scores, your favorite color, whatever. You'll be OK. Neweggg generally has much better prices than Best Buy, et al.