Do you have to go though and setup IP address and what not or will window's do that by some wizard? I wouldn't know, I never deal with those darn things...
If you do have to do it manually, with either setup, set each computer up using a different IP address... For example...
Computer 1(has internet)
IP: 192.168.1.1
Subnet: 255.255.255.0
Gateway: blank
Computer 2(pulls internet from Computer 1)
192.168.1.2
Subnet: 255.255.255.0
Gateway: 192.168.1.1
You'll probably also need some sort of internet sharing utility if you do want to share the internet. If you don't care about this, you can just leave the gateway blank. Oh, and DNS's are provided by your ISP. I don't beleive you'll need them for this setup.