For an untagged RGB image, the best option is to not convert and initially use the working RGB. Then visually and numerically (Lab or CMYK info values) inspect the image to see if the default working space is appropriate or not. You may find that assigning another RGB has a better visual and or numerical result.
https://prepression.blogspot.com/2014/06/rgb-icc-profile-roulette.html
If the RGB image has an embedded ICC profile, then you should initially honour/accept this. You can then visually and numerically inspect the image to see if assigning another profile would change the appearance favourably over the tagged ICC profile in the file. You would need to ask yourself why you don't trust this "label".
There is often no need to convert from the source profile to your working RGB, unless the source profile isn't a working space profile. If the source profile is a device profile such as a monitor, scanner or printer profile then it is best to convert it into a predictable, "well-behaved" working RGB space for further editing. One would generally convert from a smaller space to a larger space to avoid gamut clipping.
Notice that I have not commented on CMYK mode files, as they have different considerations and are generally best not converted.