Which FPGA? FreeBSD has been ported to ARM, so it should be comparatively straightforward to run it on an FPGA with an embedded ARM core. It doesn't look like there's an official Microblaze port, so using an FPGA with no ARM core will take much more work, as you'll need to port it yourself. Not impossible, but not trivial if you're not an operating system hacker.
Linux would be a lot easier - it's already been done and there's plenty of information around for it.
I'm not sure about a Virtex-7 board that meets your requirements. Have you tried Google? Have a look in some of the recent XCell magazines for advertisements from vendors.
The NetFPGA springs to mind, though this is based on the older Virtex-5. A Virtex-7 seems like an expensive option for a quad gigabit router, though!
