The properties of mounting media to be most concerned with are the refractive index and compatibility with your fluorophores. For imaging performance, I wouldn't be too concerned with hardening or non-hardening as a main consideration.
However, the difference could be important if you think you will need to unmount the coverslip. There are cases when cells need to be stained again. If it's non-hardening medium you can get the glass off to process it again. If it's hardening medium, it will be permanent.
The properties of mounting media to be most concerned with are the refractive index and compatibility with your fluorophores. For imaging performance, I wouldn't be too concerned with hardening or non-hardening as a main consideration.
However, the difference could be important if you think you will need to unmount the coverslip. There are cases when cells need to be stained again. If it's non-hardening medium you can get the glass off to process it again. If it's hardening medium, it will be permanent.
If you have an inverted microscope you should use hardening mounting medium so your coverslips do not fall off. It is also better for long time storage. I like ProlongGold which you can get with or without DAPI.
Othervise, I agree with Christopher that you have to consider the specifications of the microscope and your fluorophores when chosing the right mounting medium.
Just one little question, why don't you investigate the uptake of the nanoparticles with life-cell imaging? If you take a timelapse you see when, how and if your cells take up the particles...