FPGA board for implementing wireless video
I think reliable 1Gbit RF transmission is the biggest problem here.

Personally, I would take let's say 5-10x WiFi 11n transcievers in 5Ghz band so that you can have multiple 40Mhz channels there without interference. 

So, I would start from cheapest FPGA board and single transciever, and once you master that, you will see which bigger board you would need, it's totally depend on huw much logic you want to implement there. 

Another way to think is compressing video, or going stright to DLNA (which is basically compressed video over WiFi, standardized).