Using a NAT router alone, without a software firewall is not a good idea. Folks can google about the security risks of NAT router protection, if they wish, but to sum up, the rogue traffic that you want to be worried about is not incoming... its the outgoing traffic, just in case something does get past your AV program and installs.
A hardware firewall is a different animal and most home networks will be fine without one. You will definitely want a "smart firewall" program so that it can scan your network for known or heuristic rogue traffic and isolate your computer if it needs to. Software firewalls are especially recommended for home networks, so that your other computers and devices don't become compromised if one gets infected.
I avoided the issue earlier, but if someone is dead-set on going "free", then go with Avast. Its the best freebie on the market and one of the best paid, too. That said, its free version has failed me in the past, so that did place a black mark for it in my book.
Also, having multiple AV programs installed can cause them to interfere with each other, so install just one. S&D Spybot is a nice spyware/browser watcher, it shouldn't interfere with most AV programs.