I got the free Marvel Unlimited trial. The last thing I read was AvX, what's been good since then? I dove into the Infinity stuff yesterday.
Have you read Waid's run on Daredevil? The last three years are amazing. Hell, go back and start with the entire Bendis run since that has been the best Marvel comic for almost a decade.
Fraction's ongoing Hawkeye is great. Super delayed and inconsistent publishing, but that won't affect you on MU. I believe it has 20 issues on there and they are totally worth it.
The Fraction/Brubaker run on Iron Fist from a few years ago was amazing and must read stuff.
Rick Remender took over Captain America in 2012 and that run was really excellent. I'm a Remender fanboy, but it's as good as what Brubaker did with the Winter Soldier run.
Jason Aaron's run on Thor (God of Thunder) is the black metal of comics, and great if you like the character.
Hickman is the man right now at Marvel, and the first issue of Secret Wars is the best opening to an event in years. I highly recommend catching up on the entire Avengers/New Avengers run. I think 80% of it is on MU, and it will take awhile to get through. Technically, the premise starts with his Fantastic Four/FF stuff, but I'm not familiar enough to recommend it.
All-New X-Men is Bendis being Bendis. Skip it, unless the idea of displaced 1960s characters acting dumb is appealing.
Uncanny Avengers is surprisingly good. Dat Remender.
I really like the current Black Widow run. Same for the Punisher one.
Ellis did the first six issues of Moon knight. Good stuff.
There's universal love for the current Ms. Marvel run. I haven't touched it yet so I can't comment.
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Alternatively, start with Avengers Disassembled and go through all the major Marvel events in sequential order. That's what most of the movie content is centered on. Skip Shadowland at all cost. This is what I'm doing now.
http://www.comicbookherald.com/the-complete-marvel-reading-order-guide/