Hi & welcome to the forum.

If you want to exclude items from the search, you'll need to define that in your SearchClient conventions as described here:
https://world.episerver.com/documentation/developer-guides/search-navigation/Integration/cms-integration/Indexing/

The basics would be to create an IInitializableModule and specify your indexing rules there e.g.

[ModuleDependency(typeof(InitializationModule))]
public class FindInitialization : IInitializableModule
{
    public void Initialize(InitializationEngine context)
    {
        ContentIndexer.Instance.Conventions.ForInstancesOf<MyMediaType>().ShouldIndex(x => false);
    }

    public void Uninitialize(InitializationEngine context)
    {
    }
}

Something to be aware of though is that, by excluding items from search, that excludes them from all areas where search is used such as the search boxes above the blocks, media and file tree in the CMS so you won't be able to search for those files.

Generally I'd go for your option 2 approach unless there's a particular reason to be careful about what's being indexed.

Thanks for the help Paul

I'd have to agree with Paul on this as well.  I've been having some issues with the "remove from index" approach I had implimented, in that it would remove things that it ought not to remove.  

So I'm rewriting it to have more filters.  I am finding that the unified search is a bit trickier to filter, just as a word of warning. 

Best of luck