Firewall redundancy?

I'm on my way out, so I could not read all the posts on this topic, but my question is whether it's necessary/advisable to install a firewall program when using a verizon router with a wireless connection?

There are two computers in use:
(1) the computer that's directly hard wired to the router

(2) the computer upstairs uses an 802.11g pci wireless adapter

I recall reading that the router has it's own firewall and adding one to the system will cancel out both. Is that true? If not, should I install firewall software to both computers and what are some good programs?

 

it doesnt cancel them out. youre router firewall will drop any bad packets since youre NATed, but it allows anything going out. So a correctly configured software firewall on your laptop can block any outgoing connection attempts if you have some malware. i dont use software firewalls these days. i installed IPcop linux hardware firewall on an old box and never looked back. your router would usually be enough if youre safe online.

 

Thank-you KingSteve,
any recommended software firewalls?

 

Ive heard good things about Comodo free version. Some other people might peek in here with other recommendations though.

 

Comodo is great.