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.