Bypass download delays with Skipscreen for Firefox
As stated on the SkipScreen site, the plugin has "extra dreamy" features for Mediafire (and three others). Click a link to a file hosted on one of those sites, and SkipScreen will take care of things on its own - all you have to click on is the save file dialog box once it appears.
Whether or not you're willing to trade some future adverts for the convenience of skipping some intermediate screens is your call. Curiously, the developers also push AdBlock on their site.