Providing an embed code for images

I am trying to provide the code to embed an image on my site so someone else could embed it on there site. I am using a plugin in but am not sure that is the way to go because I have a few things i’d like to do to customize it. Two things I have in mind are dynamic alt tags so it changes the alt tags every times its loaded. Also availability of different sizes in the code.

I am not a pro at code so any help would be great but as detailed as possible would be the best option.

Thank you in advance.