First and foremost, you should probably never want to use direct image links in your SDL Tridion published content, since as you mention, then your content has a dependency on an external server.
Images and other binary content (like downloadable files, e.g. PDF and Word documents) is supposed to be stored in a Multimedia Component in SDL Tridion. Then you can directly make a (Multimedia) Component link to that from your content Component(s).
Then to answer your next question, where to store these Multimedia Components. It doesn't really matter where you store them, as the relation from your content to the Multimedia Component is a managed link. So if you decide to place the images (Multimedia Components) in for example Folder A, and later you move them to Folder B, the images references will automatically be updated (actually the image reference inside SDL Tridion is not updated, since that doesn't contain the path, but just to make it clear, you don't have to worry about them).
When choosing the best place to store these images in your CMS, you only have to consider the Authors and Editors who need to use/find them. If these images are only used for News Articles, then a Images folder under the News folder would be a good place.
However when these images could also be relevant for other Articles or content, then I would suggest to create a Images folder right under the root (Building Blocks) folder, so that every Author and Editor know where all images are stored. It will be beneficial to create a sub folder structure under that Images folder to categorize types of images when you have a lot of them. But as mentioned, you can always move the images at a later stage to another folder without having to worry about the references in the content.
