When choosing a camera, which of the following options would be the best in taking photo in low light situation and cropping photo situation?
None of these are inherently better. A larger sensor has more area to gather light, which can be an advantage when light is scarce (but which is less of a factor when it's not).
A larger maximum aperture (small f/numbers) can let in more light, but at the expense of less in focus, and again, if you have the light available, this may not matter.
Both a larger sensor and wider aperture can contribute to a shallow depth of field effect (with background and foreground blur and only the subject in fovus). That is sometimes artistically nice, but isn't "better".
And, both of these things come at a price — bigger, heavier, and (sometimes greatly) more expensive lenses and camera bodies. That might mean that even if you value low light capabilities and love shallow Dof, some actual real world camera isn't better after all, because it's too big, too heavy, and too costly.
The bigger the sensor (not to be confused with size of image (number of pixels)), the greater the area there is for collecting light, and so there is less noise produced when the signal from the sensor is amplified. This i why full-frame cameras (those with sensors that are 24mm x 36mm) are better in most conditions where amplification will cause significant noise (i.e. where there isn't much light).
The F no. is a measure of how large the aperture is compared to the focal length of the lens. The smaller this number is the larger the aperture is. Having a larger aperture is good because it allows more light to pass through the lens and so is better in low-light conditions.
Both of sensor size and aperture size have an effect on how much creative control you have over your photographs. A larger sensor will provide better control over depth-of-field and reduce noise. A larger Aperture (smaller F no.) also provides more control of over depth-of-field (in a different way to the sensor) and allows more light through the lens, allowing better photographs in low-light conditions.
The disadvantages of a larger sensor/aperture size are that these will generally make the camera larger and more expensive. A larger sensor will also reduce how far it is possible to zoom in (without making the camera a lot more expensive and bigger). A larger aperture (if not controllable) may mean that the photos have large areas that are blurred in front and behind the main focus point. This will, in fact, reduce the creative control you have over your photos.
And so, the best option for most situations is a smaller F no. (provided it can be changed) with a larger sensor size.
For DSLRs and Other interchangeable lens cameras (I'll will group them under the name of DSLRs even though they are not technically all DSLRs), this changes, due to the cost of buying lenses that cover all the situations you may need. In DSLRs it is important to consider the aspect of the crop factor, which gives an indication of how the photographs will look as compared to those taken with a Full Frame camera with the same focal length. APS-C size sensors usually have a crop factor of around 1.5 or 1.6. This means that if we multiply the focal length of the lens (e.g. 100mm) by the crop factor of the camera (e.g. 1.6) we can estimate what the field of view of the photo will be equivalent to (160mm) when compared to a full frame camera.
This means that cameras with smaller sensors will be able to have a subject appear larger than a camera with a larger sensor with the same lens.
The choice of DSLRs becomes a personal choice about preference, although for most people, the sensors of mirrorless cameras is sufficient.
Bigger aperture leads to more light hitting the sensor and requires smaller ISO values (in general) that leads to less sensor noise. But the spherical and chromatic aberrations are more due to imperfections in the lens as more of lens area is used. The price of the lens is related to its ability to minimize the aberrations.
Smaller aperture requires higher ISO values (in general) due to less light hitting the sensor. The spherical and chromatic aberrations are less as less area of the lens is used but diffraction is pronounced that leads to smoothing of images.
Each lens has a sweet spot somewhere in between.
Here is the link for reference: https://fstoppers.com/studio/fstoppers-original-what-lens-diffraction-and-when-does-diffraction-happen-6022
Obviously this is an economic question. Get a larger aperture lens first. Then if you later decide to sell your crop body camera for a pro camera, you can keep using the lens. Large aperture lenses hold their value better than camera bodies do. Always put your money in glass first.
Otherwise you're looking at reducing the benefit of the expensive (and quickly depreciating) camera by using a slow focusing, dark lens with more image distortion.
Glass first.
