A hardware firewall is also known as a router, a gateway, a NAT (network address Translation - all computers in the household have a single address known to the net; local address' are hidden). A router with rules. Rules that try to hide your household's existence on the net. It doesn't respond to pings, ports are closed, logs (incoming and outgoing) are kept, and blanket domains (sites, or domains you don't want the young ones to visit) can be blocked, etc.
Computer security, as in any defense; is layered. The more layered the better. And while layers do add a level of complexity or inconvenience to your system; once learned, layers are good.
But even that, is no substitute for smart browsing. If you use a browser such as Firefox, another layer would be something like "NoScript". An extension that allows you to temporarily or permanently allow, or disallow the execution of Java, JavaScript and Flash plugins, depending on the sites you visits. White list and black listing.
As I mentioned previously, IE and Windows, by default, are not security friendly. It is up to you to secure them through the mechanisms available to them. <
If you don't feel what is provided it good enough, look for alternatives.
Thank you!