For exactly what you need, H.264 is fine. Give it a decent data rate and it will be visually indistinguishable from ProRes at a much smaller file size. H.265 or HEVC is even more efficient, and supports HDR, but is more challenging to edit.
What’s a good data rate? Depends on the resolution.
For HD it should be around 20 Mbps, for 4k/UHD, 80 Mbps
To give you a sense of file sizes,
1 hr of HD ProResHQ is about 80 GB, as H.264 20 Mbps, its 9 GB.
1 hr of UHD ProResHQ is about 320 GB, as H.264 80 Mbps, its 36 GB
Davinci Resolve can do a good anything to H.264 mov conversion, as will Apple Compressor, or EditReady. If you want to be cross platform, then make the H.264 files .mxf