I completely agree. I'm very security-conscious; I have to be, I run ecommerce systems. I run OpenBSD (both in production and at home) - it's not Linux, but it is *nix, and just a tad more secure ;). Re Ubuntu, I can confirm that it's already far more secure with broadband than e.g. Windoze and a modem.
And I agree re a hardware firewall, for all the reasons mentioned, and a few more. To be clear, this will usually take the form of a NATing router, i.e. it separates two networks (the Internet and the LAN), and provides controlled traffic between the two. With this setup, it's the router that's online, not the clients. It will block unsolicited traffic - i.e. anything other than what you ask for. Properly setup, the benefits in terms of security of a router mean you're pretty safe from direct attack - whether with Linux, OpenBSD, or Windows.
Steve