Image and other media file management
Ari,

Let me start off by saying that media files (images, videos, etc..) attached to nodes, Meaning they are acctually uploaded when entering in a node content, those files are stored in the default file folder (usually 'sites/default/files' ), unless that field in the content type specifies otherwise. 

Example:
If i create a content type called 'blog entry', I would add a field to that content type called media.  When you get to the screen where you can edit the field information, you can select accepted file extentions, where the files would be stored in relative path to the default file location in your sites file location settings (again, usually: sites/default/files)

I would make this file location 'blog-entry/media' for this new field in my new content type. So my files would upload to: sites/default/files/blog-entry/media  when i uploaded them during the addition of content.

The thumbnail settings are somewhat default and can be adjusted under the display settings for the content type. THere are default thumbnail parameters you can select from, or you can add/remove thumnail options in the site settings as well under image settings

Once you get a hang of this flow you will see how easy it really is to manage media.

Another module worth looking into (after you have done the above, so that you may understand what the core of Drupal is doing with your media files), is the Media Module. It makes uploading and managing a little easier than core. 

Also to note: stay away from Media Gallery right now.. its a mess as of this week.. most bugs should be resolved sometime next month.