The ‘magnification’ does not have a lot of meaning on a digital microscope - if you view it on a phone screen the image size is very different from a 70" 4K screen, but the detail in the image is the same.
With a 60x or 100x objective the detail that you see in the image will be very dependent on the numerical aperture (NA) of the lens, the NA of the illumination and the quality of the lens. The theoretical resolution of these lenses may be 0.4 to 0.7 µm, but that theoretical limit will only be reached with a good lens and good illumination. @r.w.bowman wrote this about resolution and magnification. A 100x lens will usually require an immersion oil between the lens and the sample. The ‘160/0.17’ on the lenses indicates that they are designed for a ‘tube length’ of 160mm, and that they are designed to be used looking through a coverslip of 0.17mm thickness.
The working distance will be very small, usually much less than 1mm for 60 or 100x . The sample should be under a coverslip on the same side of the slide as the objective lens, so the slide ‘upsidedown’ on an inverted microscope design like this. It is possible to get objective lenses with long working distances, but they get expensive very quickly. They are often designated ‘metallurgical’ instead of ‘biological’ lenses, and are not designed for use with any coverslip or glass between the sample and the lens - they are for looking at metal and mineral surfaces. There is one I found that is not too expensive, and also is designed specifically to look through a microscope slide from underneath, so with 1mm of glass, and with a working distance of a few mm. Motic Microscope LWD 40x Plan Objective Lens (motic-microscope.com). It is 40x so has a larger field of view than 60x, but at 0.5NA the theoretical resolution is still about 1µm. I have a couple of Motic microscopes and the lenses are pretty good, I have not yet tried this particular lens.
See also this thread Comparison of a pi-camera and a 20x optical lens - Contributions - OpenFlexure Forum which has some 40x and 50x at the end.