Well, might not be worth it really.
If you are using SATA drives that limits you to SATA II, or 250MB/s maximum (200 or so in practice). Your internet speed maximum should be 143MB/s or so. There are very few places that will offer you that much bandwidth to a single endpoint. Such internet speeds are for multiple users.
A 1Gbps ethernet connection will generally get you around 80MB/s
So you would need a 2.5Gbps network card.
Your motherboard appears to be PCIe 1.0. All of the 2.5Gbps ethernet adapters I can locate quickly are PCIe 2.0, so you would lose half the bandwidth and basically be back at 1Gbps.
If you can locate a 4x 2.5Gbps card, that might work.
In addition, you may run into the DMI speed limit. Everything that connects the PCH to the CPU generally goes through a single DMI connection and this may not be fast enough to handle everything at once. You can avoid that by using the primary x16 slot for your network adapter, this will be CPU connected.
And finally, downloading at high speeds actually does require a lot of CPU processing power. Given the age of the system, this may not work so well and you could end up with fast downloads, but an unresponsive PC experience.
(It was actually quite common for complaints to come from new Google Fiber adopters, too slow of hard drive or too slow a computer to realize the maximum bandwidth)