First, reading the original post and all these replies, yes you can have as many computers as you want hooked into one cable modem.
Now, you mentioned splitting your signal. You cannot split the cable from the wall like you would for a tv. One cabe from the wall to one cablemodem for one billing price. You can hook a router from the cable modem to the computers through wires or wireless. WEP is good, but WPA is better. Fez, i don't know what wpa stands for, but i have a passkey. You can also use a radius port. Basically, between wep and wpa and wpa-psk, its just a passcode to get into your router, like "new england clam chowder" from ace ventura.
I've got a D-Link wireless g router, the DI-624 ver. c2. If you have the wireless portion secured both from the router and from the wireless computer, you should have no problem. As fez mentioned, its easy to break into wireless networks that are left unsecure. Just last night, my wife's computer crapped out momentarily. In checking with the wireless software on the computer, i was able to connect to my neighbor's wireless connection and view their computers! I could have moved the printer drivers to my computer and printed to her computer "GOTTCHA!". Thus, its VERY IMPORTANT to have your wireless router secure, zone alarm or not.
Linksys, Dlink, Belkin, are all good brands. I use broadbandreports.com in the forums section to get ideas. Go there. However, product reviews seem to be all negative and bitchy. Take it with a grain of salt. These people could find something wrong with a bar of gold.
For a novice, with some PRE PRINTED directions (you won't have internet while you're in the process of all of this), you're looking at an hour worht of hardware install (running wires, installing PCI/PCMCIA cards, etc.) and an hour worth of tweaking the drivers and firmware for the devices. If you need help, PM me and we can get together via e-mail or whatever messaging service and i can run you through the setup, or what to buy.
Oh yeah, if you run to the store, just remember to pick up at least 2 cat-5 cables of at least 6' in length... trust me on that one.