Hi, We have a great solution for this. In fact two options whichever suits you:
Drop box. and using the API you can manage the files, remove or add new files.
Other method which is even more efficient and fulfill your requirements upto 100% is making at your own hosting. You need not to do anything, we'll design a portal for you within the same price and time frame and you need to buy a $15 hosting from the godaddy. Rest of tasks will be done by us and you can easily view, upload or remove files remotely , even if you are at phone .