Why you want to avoid Dynamic SQL in stored procedure?
There is nothing wrong with using dynamic SQL if you must. In fact in some circumstances it is the only option that you have. It is more of a recommendation not to use it as yes it can lead to a SQL injection if your input is not sanitized, and yes using dynamic SQL in modules that get called often can be detrimental to it's performance. 

I don't think there is a concrete example as per se but I would say this: Try to achieve what you are after using regular queries and statements first - only then once you have exhausted all other avenues do it dynamically. Just remember that executing a dynamic SQL string is done in a separate user session to the module that is calling it - so you may encounter permissions issues where you are not expecting any. 

If your worried about performance; test it. If your worried about security; validate your input. There is no right or wrong - only that you use your best judgement based on the information and tools you have available to you at the time.