What is it that the plugin doesn't do for you? I ask as I've got the same requirement (bar the widget), and I've managed to get Downloads Manager to do it for me. It isn't brilliantly written or supported, and looks like it needs some work doing to be fair.
What I found using it was that it gives you the option to offer a download link (i.e. a url with normal text in like blog.com/filename rather than blog.com/?file_id=2). On my install if I ticked this option, it didn't work. This could be due to my setup (multiple blogs with different domain names), but regardless if I left this off, it worked fine. You also need to upload the file first, then fill out the form, and highlight the file name on the right hand side. Bit messy, but it does work thus far. Finally I had to make sure the plugin directory had write access to the file system, as this prevented both uploads (it puts them in its own directory) and changes to the table templates for the plugin.
The sidebar widget would need a little development work, as the default options for listing (i.e. showing the list of uploads) are in ascending date order, oldest first. I'm going to have a little play about with the plugin today to see if I can query the list in a custom fashion.