Do you mean you want to reuse a skeleton and all its animations, but use different images to make it into a new character?
You could save the whole project as a new project file, or you could duplicate the skeleton in the same project. You'd then modify the skeleton as you need for the new character. This has the downside that your skeletons are separate, so changes to one don't affect the other. For example, if you add new animations, you'd have to do it twice. You can bring animations from one project into a different skeleton using Import Project > Animations, but there are some limitations.
If you use skins, then you would really be using the same skeleton and animations for both character. If you need bones only in some skins, you can use skin bones. If you need to move some bones for some skins, you can use skin constraints. Check out this blog post about that:
Blog: Skin constraints for different proportions
As for tips, some are described here:
Skins - Spine User Guide: Skin workflows
