I have bought a bunch of FPGAs years back when I had more time maker/hacker stuff, but then I haven't done anything with them. This looks like an interesting use case that would allow me both to know more FPGA bits and the actual use case of computer systems...
You're going to need a high performance part (expensive) for that.
I am in the same boat, I have a $150 FPGA dev board I haven't really done anything with, though I have an Arduino project would would probably be a good fit for it (a display controller for persistence of vision displays)