Secret Wars (1984) is one of Marvel's first and most beloved events. For an book designed to sell toys, it has a surprisingly great story. If you're just interested in Secret Wars (2015), it's not at all necessary though. There similarities between the two, but they are very loosely connected.
Secret Wars II (1985) is a much sillier book. Think of it like the Marvel version of that Star Trek movie where they go back to the 80s to rescue whales. It's a fun book, but is largely ignored by future writers.
Secret Wars (1984) and Secret Wars II (1985):
27 years later, the seeds of the 2015 Secret Wars by Jonathan Hickman began in his series Avengers (2012) and New Avengers (2012). These books were designed to be self-contained, but tended to bleed together. If you want to read everything leading up to Secret Wars (2015), this is where you should start.
It's daunting in size, but even before Secret Wars, this leads in to the acclaimed event Infinity. The entire series below is one of the greatest comic stories I've ever read, and I highly recommend the whole thing if you have the time.
Avengers (2012) and New Avengers (2012), in reading order:
This is where the real lead-up to Secret Wars begins, and things start to get serious. If you want some backstory to Secret Wars but can't do all of Avengers / New Avengers, this is a great place to start.
Here's Hickman's Time Runs Out lead in to Secret Wars:
Also available in a single huge hardcover:
Finally, don't be shy to just start with Secret Wars. The hardcover contains a convenient Secret Wars (2015) #0 which is designed to be an introduction to the event:
If you want to know more about the lasting existential and omniversal effects of Secret Wars, I recommend the series The Ultimates (2015). If you just want more alternate-universe battles, check out Contest of Champions (2015):