New modem or router ?

I'm not clear on this. You want to have 2 computers on the same internet connection but you don't have a router yet? So that means no network. Why not just set up a home network? It's very easy these days. You'll need to buy a router. The price on your links looks to be about average. You just need to decide what you want to do with it. Having the router will form a network allowing you to share files between computers. The second link you have there is a wireless router. These are nice for eliminating wires, but they are not as fast or reliable as wired imho. The wireless router will have some Ethernet ports on the back as well allowing you to use it wired as well as wireless. I have a wireless router and use it for both wired and wireless connections. My desktops are in the same room as the router so they're plugged into the router via ethernet. I use the wireless feature for my laptops. This is the route I would go. It would allow you to try both wired and wireless connections to find what's right for you and they're about the same price as wired routers. The router has a special port on the back to plug your modem into. This will give all computers on the network access to the net the same as they would if the modem had another port on the back of it. One other thing to consider is the speed you want your network to run. They go from 10Mbps to 1Gbps. Wireless is 802.11b,g or n. N is the fastest.