I might be changing from dial-up access to either DSL or Cable modem connection. The ISP will be determined later after i've priced out all the competitors. My question is will I need to install a NIC in my desktop PC in order to connect to the internet via cable? Right now all i have is a winmodem installed in a PCI slot.

Yes you will need a NIC card in a PCI slot. You can go with USB if you cable provider offers it. I do not recommend USB unless you do not have an empty PCI slot.

Also, if my roommate and I want to share that one cable internet service, will i need to buy a particular type of router?

That would be the best setup since you can share an IP address and not have to be charged for a second for your niehbor. See the diagram for a Linksys router and how to configure it.

http://www.cable-modems.org/articles/linksys_review

3rd question is how will a Pent II (450 MHz I think) OS=Win 98 SE run on cable internet service? I told the person who asked me this question that it should be just fine. I guess she was thinking since its such an "older PC" ... she might not notice much of a difference compared to dial-up. I told her it's more a function of connectivity rather than the CPU. Which is only partly true since a 2 GHz CPU would allow you to process the webpages faster compared to a 450 MHz CPU. Anyone agree on this?

The CPU has very little to do with your access speed which will be a substantial increase.