Media File Folders and Using Host File Manager

For a website I’m building I have a lot of images and pdfs that need to go on the site. I’ve been using the wordpress media library to upload files and put them on the site, but I don’t like that I can’t create separate folders for “images” and “pdfs”. I also can’t change the URLs to be more SEO friendly, such as http://www.site.com/pagename/filename because any file uploaded through wordpress automatically goes in the media folder so that it’s http://www.site.com/media/filename.

Since WordPress doesn’t have this functionality, I’m trying to use the file manager on my hosting control panel to put all the media files in the folders I want them in. But I can’t figure out how to then easily get the files onto my site. I have a theme that allows me to quickly put in images without using wordpress media uploader by putting in a URL, but I don’t know what URL I would use since the files are stored in the file manager.

Help on this? What’s the best way to get images/pdfs and other files onto wordpress site without using the uploader? Or is there some other way to create custom URLs and create multiple folders for media files to be stored in?