I think most network cards will auto-negotiate these days. In general though use a crossover cable through when connecting "similar type devices" and straight-through when connecting "dissimilar devices". I am not going to get into the technical details here, but in general:
Computer <----> Computer : crossover
Computer <----> Router : crossover
Computer <----> Switch : straight-through
Router <----> Router : crossover
Router <----> Switch : straigh-through
Switch <----> Switch : crossover
Also bare in mind that most home routers are not really routers, meaning that you cannot assign different IP addresses to each of the ports that you see on them. They are three devices in one. The Ethernet ports that you see on your router are switch ports really, so you can use a straight-through cable to connect to those.
If your NICs won't auto-negotiate and you do not have a crossover cable, use a switch/home router and two straight-through cables. That should work.