For gameplay recording @ 4K with 60 FPS, use Nvidia Shadowplay.
Video tutorial too:
https://www.youtube.com/watch?v=oqu0O2wJgAo
If you're AMD user then here's further reading,
link: https://linustechtips.com/main/topic/624493-best-program-to-record-4k-60fps-gameplay/
As far as file size goes, that depends on the duration of recording. The longer the recording is, the bigger the file size. But i can tell that it will be huge.