I just use my router and I have the windows firewall on each of the pc's. I had Zone Alarm but that's just TOO safe! It doesn't let you do anythign! I would not recommend ZoneAlarm if you have networked PCs.
Sygate is different. It does ask you if you want programs to access the internet, but it remembers. link: http://smb.sygate.com/products/spf_standard.htm
If you use two firewalls they will interfere with each other. You could lose your connection to the interenet, slow down.. Etc.
Not between hardware and software. Yes, two software firewalls will interfere, but not a software and hardware one. And Windows firewall and another one like Sygate will not slow you down that much..