Mediafire is a very old file hosting platform. You can expect them to stay around for awhile as well as they are very compliant for the US Government so the idea of the same thing happening to MediaFire is pretty unlikely.
Then again, that also means you lose some freedom, and it could be a little more risky to host your own files there if they were accidentally identified as DMCA material. Mediafire and a few others have been known to remove anything that has links on a blogspot blog or other locations, so you have to be careful if you don’t want your files deleted.
Overall, so long as you keep everything private you upload to Mediafire, it’s a good host that could definitely meet your needs. The only real downfall of Mediafire is that it’s centralized, so if Mediafire goes down your files could go with it.
For a more open environment for your files you can learn to upload to and download from Usenet. With retentions the way they are you can almost expect any file you upload to be around for a very long time. (Downloading & First Setup Tutorial, Uploading Tutorial)