If you have nForce3 and its native GbE NIC, then you should use that -- it's excellent. (I suggest "Optimize for" = "Throughput" with this NIC unless you're running in a very high CPU utilization scenario, where the other option might be better.) There are some kludged nForce3 motherboards which don't have the nice nVIDIA GbE, and I guess if you have one, you could try whatever GbE NIC they supply, if any, or try installing e.g. an Intel Pro/1000 PCI NIC.
I don't have any experience with the VIA NIC, but if it is a PCI NIC, then I'd guess the odds are that's it's an inexpensive under-performing NIC, and you'd be better off with an add-on Intel PCI NIC, for those cases where the NIC actually makes a difference.
Neither of the PCI-based NICs IMO are a good idea if you're running a PCI RAID controller. If you have on-board non-PCI, certainly use that; perhaps consider using the on-board SATA/IDE instead of an add-on PCI controller.