Design advice: Radar interface
The big unanswered question is what bit resolution (and implementation noise figure) you need.  

In the unlikely case that this is limited to around 8 bits, you are basically looking at a digital sampling oscilloscope front end.  

In the more likely case that you want 14-16 bits, you are looking at a wideband software defined radio sampler, though without the usual continuous reception requirement.  

Lots of designs for both are available - mostly consisting of an ADC, an FPGA of some sort, potentially an outboard buffer memory, and a USB interface.  For a one-off, you'd be better of buying than building, unless the learning experience of doing it yourself is a higher priority than the cost, timeliness, and capability of the result.

If you go with an SDR front end, you may need one that can be customized, since your bandwidth may exceed the continuos streaming capability - instead of the normal decimation to a lower bandwidth (and higher resolution) before streaming, you might instead want to do periodic snapshots at full bandwidth, which could necessitate an FPGA code change.  This would point towards some of the open source platforms over proprietary ones, unless you find one already made for burst usage.