JChui,
Here is a link to a web defintion of "What is a router?"
http://isp.webopedia.com/TERM/r/router.html
Generally, on a standalone computer, you don't need a router and a firewall. Routers are normally used to connect multiple computers on a LAN (Local area network such as one you might use within your home or small business) to other networks or to your ISP (Internet Service Provider).
Although ZoneAlarm is a fairly good software firewall, but be aware that it's not perfect. Even the best secured sites have been hacked into. It's just another possible tool in a secure system. Your best bet is to do some research on computer security, firewalls, antivirus programs, spyware, and anything else you can think of. It's a good thing to know as much as possible about this issue.
Hope this helps.
Grif