Ok, let's clear up a few concepts here.
Onboard Gigabit Ethernet controllers are provided by a wide range of manufacturers and come with either a PCI or a PCI Express interface in modern computers.
On a cheap motherboard you'll get the type that interfaces with the PCI bus and this bus doesn't offer enough bandwidth for the full Gigabit speed.
The PCI Express bus on the other hand has more than enough bandwidth for Gigabit Ethernet. However, the various controllers available offer different performance and some might not hit full Gigabit speeds.
In reality, if you have an Intel controller on your motherboard (which isn't that common sadly, as they're expensive) then you're fine.
Marvell are generally known as a good source for Ethernet controllers as well as Broadcom. The most common brand of Ethernet controllers are Realtek and they're a bit hit and miss depending on the model.
Many motherboards with dual controllers allow for teaming, although from what I've seen this only tend to be with Realtek or Marvell controllers if I remember right.
For something faster you'll need a space x4, x8 or x16 slot (make sure it actually delivers the bandwidth as well, as some slots offer far less bandwidth than the physical connector suggests).
Intel has a 10Gbit over copper card http://www.intel.com/Products/Server/Ad ... erview.htm
but it's in excess of US$500 which seems like an insane amount of money to pay. You might as well invest in something like infiniband then, as it'll offer better performance for a similar price, although I'm not sure if you can connect two cards to each other without a switch.
Dual port Gigabit Ethernet cards can be had cheaply and you can even pick up a quad port Supermicro card with Intel chips on it for less than $200. http://www.supermicro.com/products/acce ... -UG-i4.cfm
I think going with a quad Gigabit Ethernet connection you'd have more than ample bandwidth, as I can't see you exceeding 512MB/s when you're copying files (minus TCP/IP overheads, which I guess takes it down to about 500MB/s).