Interfacing FPGA and a storage device
We've just built a logger with a data rate of that order of magnitude.  The data are captured on an FPGA and then sent over to a PC using USB3.0 which then writes it to disk.

Assuming your logging latency is not critical (which it usually isn't) I imagine you could do the same.

If you use an Opal Kelly FPGA board, the HDL interfaces and driver development are very straightforward.  I have no connection other than as a satisfied customer!

Alternatively, using a PCIe plugin card with the Xillybus driver provides another straightforward HDL and driver experience. 250MB/s is pushing it for a single lane of PCIe, but as you say a x4 interface will be OK.

Or the full-custom approach of building it all from scratch is of course open to you if you have time, but no money.  I'd still build something to interface to a PC though, rather than trying to go direct to disk from the FPGA.