Thanks for your interest in the plugin and for your question. Here are a few suggestions that might help you get what you want.
The example shortcode you gave in your bullet list is a good start, but as coded it will only select images, the default MIME type. You can add
post_mime_type=application/pdf to get a gallery of PDF documents.
mla_style='default' parameters are not necessary because 'default' is, well, the default.
You might also want to add
size=icon to your query, which will give a nice little thumbnail image for PDFs. Here's another example:
[mla_gallery post_mime_type=application/pdf post_parent=all size=icon link=file]
The parameters in the above example select just the PDFs (post_mime_type=application/pdf), show all of the PDFs regardless of what post/page they are attached to (post_parent=all), display an appropriate icon (size=icon) since PDFs are not images and makes each icon a link (link=file) to the corresponding PDF file.
The PDFs will be listed in the gallery even if they are unattached, and the Caption field will be displayed under the icon for each file. If you omit the size-icon parameter you will get a text link in place of an image. To filter the list by "Att. Category" you can code:
[mla_gallery attachment_category="brochures" post_mime_type=application/pdf post_parent=all size=icon link=file]
Note that you must use the internal name for the taxonomy and the slug value(s) for the match. See the "Taxonomy Parameters" section in the documentation for more details.
The Settings/Media Library Assistant Documentation tab has lots of information on other
[mla_gallery] parameters you can use to select items in different ways and display different results. Here are a couple of links to Support Forum topics along the lines of your question:
For a "ul"-style gallery, here's another approach. Change your shortcode to look like this example (all on one line):
[mla_gallery attachment_category='brochures' post_mime_type=all link=file size=none columns=1 mla_float=left itemtag="ul" icontag="li" captiontag="span"]
The tag parameters give you the bulleted list. The columns=1 and mla_float=left avoid a centering problem.
I hope that gives you a good start on your application. Let me know if you have any other questions or problems.