In both cases, you will need to install OS/2 drivers for the network card that is installed in your PC. Then install TCP/IP; configure it to get an address from a DHCP server. Before you start copy down all the server names & addresses specified in your Windows settings. Most of the traditional TCP/IP configuration fields will be blank because the values are retrieved from the DHCP server.
You may need to update your TCP/IP stack to get it to work with Cox. To check the version, run inetver at a command prompt. The original Warp 4 TCP/IP stack returns version 4.02e; the latest is 4.02r. The TCP/IP update is available at ftp://ftp.software.ibm.com/ps/products/tcpip/rsu/stack/latestv4.html. This may not be necessary, and there have been some reports of difficulties with it, so I would not update unless necessary.
Southwestern uses a standard TCP/IP setup with addresses assigned by a DHCP server. It works with the TCP/IP stack that shipped with Warp 4.
However, RoadRunner has an additional hurdle that Cox users are spared: you must login in to an authentication server after you get your IP address. The authentication server is between you & the Internet. Before you login it blocks TCP & UDP packets. This means you can ping any computer you want, but you can't surf the web, get e-mail, or do anything else very useful.