No one can really give you an answer because the answer is completely dependent on your lighting set-up, as Michael C commented. But, you have some wrong assumptions that I wanted to point out.

There are two types of set-ups you might use, continuous lighting or strobes.

Strobes

Shutter speed is relatively slow

Maybe correct, it really depends on your definition of "relatively." You'll be limited by your camera's flash sync speed - but shooting slower than the max sync speed won't hurt you. You'll probably be somewhere between 1/60 and 1/125. Keep in mind that shutter speed does not affect exposure in 100% strobe set-ups, so as long as you're under the sync speed, you're fine.

Aperture doesn't need to be so wide (My uncle suggests a F-stop of around 5.6 to 6 because lighting is good, while my father said that it didn't matter how high the F-stop value was because there was good light and that there was a white background. Although I do think it is better to have a blur on the background despite the white to kind of make it easier for editing and not get too much background noise while not having a too low aperture).

Your aperture is controlling DoF and has the typical image quality constraints of: most lenses aren't too sharp at their widest and diffraction will become a problem at some point while stopping down. You need to be be using the aperture that will get you the DoF needed for your shot given your product size and focal length and how you're shooting.

You will balance your aperture selection with ISO and strobe power. However, if you hit a wall in one of these, something has to give. For example, if using very bright strobes set at minimum power, ISO100, and f/4...and your image is too hot - then you have only two choice - easy choice: stop down...harder: find a way to diffuse the flash more.

Also, white is white. If you're going for that blown-background-product-look - there's no point in going for background blur - there's simply nothing to blur. Noise is not related to aperture. If you want a low-noise shot, keep your ISO down, and if using a Canon, don't ever use +1/3 stop ISO's.

ISO is set as low as possible (100 in my case)

This isn't a bad idea, generally speaking. But you may have to balance this with your strobe power and aperture needs. Modern cameras show very little noise difference in the lower ISO's so don't be afraid to push this up if needed.

Continuous Light

Shutter speed is relatively slow

Continuous lights tend to be of less power. I backed OrangeMonkie's Foldio and can tell you that, though the light appears good to the eye, it's very, very low. So now you've got a problem: either use a tripod for every shot (great for when you have a workflow, harder when you're trying to experiment) or realize that you'll have to sacrifice DoF or ISO because unlike strobes, shutter speed plays a part in your continuous light exposure.

Aperture doesn't need to be so wide (My uncle suggests a F-stop of around 5.6 to 6 because lighting is good, while my father said that it didn't matter how high the F-stop value was because there was good light and that there was a white background. Although I do think it is better to have a blur on the background despite the white to kind of make it easier for editing and not get too much background noise while not having a too low aperture).

Again, you need to be using the aperture that gets you the DoF that you need. However, you are balancing this with your shutter speed and ISO needs and if your continuous light source isn't powerful enough, then you have to start sacrificing. You could sacrifice DoF for exposure. Also, white is still white - stop worrying about blurring a blown background.

ISO is set as low as possible (100 in my case)

Low-as-possible with continuous light will likely be higher than low-as-possible with strobes. But, this completely depends on your lights and how powerful they are.

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TLDR; the types of lights that you use and how powerful they are in addition to your photographic needs directly impact the "short list of values" for exposure. If you posted an example product and the size of your location, we could help you figure out your ideal aperture for DoF needs. But without chosen lights, no one can help you calculate your exact exposure or even the short list of values because it could be all over the place.

TLDR2; Don't trust your family with photographic exposure problems.