Format choice sounds like a detail. It changes results enough to be worth thirty seconds of thought.
Start from the least compressed file you have
JPEG throws away detail in a specific way: it works in 8x8 blocks and discards fine variation within them. Around a hard-edged watermark, that produces visible ringing — faint echoes of the mark's edge spread into nearby pixels.
This matters because the repair has to remove the mark and its compression halo. If you have the PNG, use the PNG. If you have the original camera file, export a PNG from it rather than reusing a JPEG that has been through several rounds of saving. A screenshot of an image is nearly always worse than the image.
Save to PNG if you are going to keep working
PNG is lossless: what the tool produced is exactly what lands on disk. If the cleaned image is going into an editor for further work, save PNG, always. Saving to JPEG at this stage bakes in compression that the next edit has to fight.
Save to JPEG or WebP only for publishing
When the image's last stop is a web page, JPEG or WebP at high quality is sensible — the files are much smaller and, at quality 85 or above, the difference is hard to see. WebP is smaller again for the same quality and is supported everywhere that matters now.
The rule is simply: compress once, at the end. Every intermediate save costs quality you cannot get back.
Transparency
If your image has an alpha channel, PNG or WebP are your only options — JPEG has no transparency and will flatten it, usually to white, sometimes surprisingly.
A note on resolution
Do not downscale before removal. A repair has more real texture to work from at full resolution, and downscaling afterwards hides any remaining imperfection. Doing it the other way round enlarges every flaw.