I am using AdBlockPlus and NoScipt in Firefox which gives me perfect control on what scripts are running at least from my perception. Firefox is a bit slow though if you use a lot of tabs. For Downloading I use DownThemAll which works with most of the providers.
You can use OneDrive as an alternative for sharing files. Microsoft is very strict on data privacy. And for me it works pretty well usability wise.
I got captcha's but not very often. With the above config I never got any popups. I had to allow skripts from mediafire, but have not allowed any other scripts in order to be able to download files.