<< Does a router work as a network hub, or does it just split the cable connection? >>
It depends, I have a Linksys BEFSR11 router, it only has a port to connect to a cable modem and another port to connect to a hub/switch. You can also buy a Linksys BEFSR41 or the new BEFSR81 that has a port to connect to the cable modem and either 4 or 8 ports respectively to connect to the other computers in your network. Since you already have a hub, stick with a single port router like the Linksys BEFSR11 or the Netgear RT-11 and connect it in between your existing hub and new cable modem.
<< Which is the best way to go? >>
Personally, I went with the router since I did not want to have a computer on all of the time (server). My cousin, however, went with a server setup and is running Home PNA to connect all of his computers! Of course, running a dedicated server means that you must also find and configure either Windows98SE's Internet Connection Sharing or some other proxy server software. Also, if the server ever does go down then all of your other computers loose their gateway to the internet.