A standard asynchronous serial interface isn't normally chosen for a high speed data acquisition system.
This goes for any external memory chip as well as uploading the results.
A microcontroller with lots of RAM, or with the ability to talk to an external parallel RAM chip would
be my choice. Some can directly interface DDR memory (but that's all high speed surface mount
stuff).
This might be better suited to a full blown compute engine like a RaspPi.