ps. You can spend 400$ on a hardware raid card with 8 sata ports like this one : http://www.newegg.com/Product/Product.aspx?Item=N82E16816151137
Add ~150-200$ on cpu, mb, case and ram and optionally get a 2-4 port gigabit network card from eBay and do port trunking. The software's going to be a problem though, there is freenas and other ready made solutions but it's still not going to be as polished as that Synology comes from the factory.
For the task at hand, I would say hardware RAID is a big no-no. It's expensive, you're not targeting high IOPS, and now your data depends on having a working RAID card of correct model and firmware. You can get an 8-port SAS HBA for under $100, if you even need one, since the 6 or 8 onboard SATA ports common these days are likely to be sufficient, at least to start.
This guy did it recently with a pretty nice build for around $400 sans-drives. I would personally throw in an Intel PCIe NIC just because onboard NICs suck, but hardly required.
Also keep in mind that port-trunking/link aggregation chooses a link based on a hash of some portion of the header (often just the source/destination MAC addresses, though sometimes layer 3 or even layer 4 on higher-end gear). In other words, you're primarily concerned with throughput to a single client, this won't help at all, since all the traffic will end up on the same link.
Nas4Free is pretty polished these days, and gets you ZFS, which is hands down worth any slight increase in effort required over a commercial product. Automatic scrubbing and block checksums are exactly what you need for long-term archival. Snapshots, and ones which can be incrementally copied to a remote system by sneaker- or Inter-nets would also be pretty handy. Most of the commercial boxes are based on standard Linux technology, so you can plop the disks into any machine to recover your data if the NAS box goes tits up, but a nice benefit of building on Nas4Free/FreeNAS/Linux is that you
know you can do this in a pinch and that the vendor isn't doing something weird (like Drobo and presumably others).
Edit: Ninja'd but I'll leave the post anyway