Are superhero games an acceptable option? If so, I'll recommend the
Sentinel Comics RPG as a good fit for the stated parameters.
It's a bit of a deceptive game in some ways - big 425+ page book, over a quarter of that tied to detailing the company setting (which essentially carries the card game timeline forward past the Oblivaeon boxed set), and huge blocks of space devoted to what look like complex character generation tables for both heroes and villains. Sounds all wrong for an easy to learn, quick-playing, versatile system, right?
When you actually dig into it, you'll discover that what real complexity there is mostly gets front-loaded into session zero. The character generation system takes up a ton of pages and is a bit time consuming, but it's broken up into five stages with a limited number of actual choices from limited menus in each stage so analysis paralysis is minimized and once you're done with your character sheet you're never going to look at any of this stuff during play, and only rarely as characters grow and change over time.
With the PCs made, their players really only need to understand about fifteen pages worth of game mechanics - and that count includes actual play examples. Once you get used to what the six basic actions let you do and how your abilities modify them you'll only rarely need to look at anything that isn't on your character sheet, and you can build a very cheat sheet just by copying over the boost/hinder/overcome results charts (which use the same numerical brackets for results) onto your PC sheet or an index card, maybe adding the mechanics for minions and lieutenants and your own GYRO zone tracker with a paper clip as well.
The GM has a little more to deal with in terms of reading, but again most of its only gets referenced in prep and won't be needed in play. Unless you play very long (6+ hours) sessions you'll probably only need to prep one-three action scenes at a time, and if things go in unexpected directions slapping an impromptu one together on the fly isn't hard - certainly easier than in most games I've run. When you're at the table the simplified mechanics for NPCs (especially minions) make it easy to handle their actions, leaving you time to be descriptive about introducing twists (environmental or otherwise) and explaining non-combat challenges that need to be overcome.
The game engine also isn't at all tied to the Sentinels setting, and can easily be adapted to homebrews or other published comics (eg Marvel or DC). When the game was new fan base produced quite a few very unofficial ports for published characters, most of which can still be found online, although not on the company forum. There are also hundreds if not thousands of homebrew villains out there if you don't feel inspired to create your own or just want some mechanics to re-skin -
my own blog's got 250 of them, and there are many more on the
GTG forum.
Sales pitch aside, there are a couple of potential deal-killers with the game. First, it's really written with the expectation that you'll have at least 4 players, and doesn't scale downward from there particularly well. Three PCs is barely doable, two is a serious strain, and doing one-on-one just doesn't work without modifying things. Second, you may find it increasingly difficult to challenge players meaningfully once they start reaching double-digit collection counts, which happens after 60 or so sessions and gets steadily worse as the count climbs, so a bit over a year of weekly play. That may not be good for you depending on how long a campaign you want, and I've yet to see a good solution to tweaking scene design rules for "high level" play.
Other than that I think this fills your request pretty perfectly. Worth a look, anyway. If you wind up tweaking it to use for the Rifts setting (which is honestly no weirder than most superhero games) I'd be curious to see how it came out.
