This is perfect

A clean and simple way to do just what it says — list your files. You can tell it which directory you want it to point to. Just insert the shortcode and you’re done — it also has a bunch of useful parameters you can pass, like how to sort, whether to display file sizes and icons, etc. The display is in a clean attractive table.

It also has an upload functionality but for member-based file uploading on the front end, I would suggest using something like Gravity Forms (file upload field) with a hook in your functions file to put all uploads into the directory that list-yo-files searches.

Anyway thanks for a great plugin!