[Updated December 2012]
The default is “None”: if you prefer one of the other options, you’ll have to click the relevant tab. The tool will remember your last choice, so you only have to do this once (as long as you don’t want a different option in another post or page).
To change the link status of an image after it has been uploaded and inserted, you go to the Visual editor, click on the image, click the edit button that shows up (the mountain icon), click “Link to Image” (or “None”, if what you want is the opposite), click Update. To turn a linking image into a non-linking one, in particular, you can also click on the image (in the Visual editor) then click the Unlink button of the editor.
Attachment pages are a strange invention. They are automatically created, but they are not permanent, and they don’t get included in your list of pages, so you have almost no control over them. You can change the page title (the default is the name of the uploaded image the way it comes up in the URL), but you can’t change the alignment or the borders of the image; and… visitors can leave comments.
Currently there are two ways to disable commenting on attachment pages (as well as on gallery “carousel” slideshow images):
a) Disable commenting in Settings > Discussion, upload and insert the image(s), then enable commenting in the Discussion module of the post/page editor. If you’re not seeing the Discussion module while on the post/page editor screen, click Screen Options (top right) and check “Discussion”. You can also enable commenting if you go to Posts/Pages > All Posts/Pages and click Quick Edit (under the post/page title).
b) Upload and insert the image(s), then go to Media > Library and edit each image to disable commenting in its own Discussion module. Again, to make the Discussion module show up, click Screen Options.
The chief merit of attachment pages is that you can include notes on the image. You write these notes in the “Description” box that shows up after you upload the image.
Note that the description box is not available when you click the edit button of an already inserted image – not even in the “Advanced Settings”: if you want to add or edit a description for an image already uploaded and inserted in a post or a page, you must access it via the Media Library. When the “Post URL” option has been selected, you can also access it via the “Edit” tab of the attachment page.
Both the attachment pages and the full-size originals can be made to open in a new browser window, as in the examples above. Unfortunately, this option is not available when you initially upload and insert an image – you have to do it afterwards: you click the edit button of the image (in the Visual editor), click Advanced Settings, scroll down to Advanced Link Settings, tick “Open link in a new window”, click Update; or you add the relevant piece of code in the html editor (see here).