Regarding Marvel;
If you want a general overview of the main, core stuff in the MU, Civil War and Secret Invasion (the main series on both) are musts. Like 'em or lump 'em they definitely changed the Marvel universe. Secret Invasion, being the most recent one, will give you the most up to date account. After that it's the Avenger's titles, starting with Dark and then New Avengers. Mighty Avengers was up until SI, really relevant, now as good as it is, it's following it's own tangent.
Since the start of New Avengers #1, several years back, Marvel have really placed an emphasis on the Avengers being integral to the wider Marvel universe. Civil War split the Avengers into two camps but the Avengers remained essential reads for a comprehensive understanding. Secret Invasion pushed this to a greater degree by adding another team, Dark Avengers (By the way if you like this series, read Warren Ellis' run on Thunderbolts, it's exactly the same).
If you aren't too bothered by keeping up with main events and just want good Marvel stories, then I'd recommend....
Captain America (Ed Brubaker's run) He's approaching the 50th issue but I'd recommend picking up the past 40 something issues in trades (You must buy up to #34 for a comprehensive look at Cap's wider role in the MU up to today)
If X-men is your thing then I'd recommend Messiah Complex. Up until New Avengers #1 came out, the X-men were Marvel's main super team and they had some really good (and really bad) events. Messiah Complex feels like one of those fun events from a decade or two ago. Also it's important for upcoming X-men events so it's a must for X-men fans.
If you really don't care about the Marvel universe as a whole and would rather just enjoy a character cutting out their own corner of the universe, Iron-Fist is a good recommendation. Ed Brubaker and Matt Fraction did two trades on that which is overflowing with Kung Fu action.
If you really don't want continuity and just fun stories, pick up Ultimate Spider-man. It's set in the Ultimate universe which is outside the main Marvel universe and follows it's own route. It's really fun and you can just grab any trade (I'd recommend starting around issue #70 or #80, and work through the clone saga storyline).
Also from the Ultimate Universe, I'd recommend the Ultimates. DO NOT READ Ultimates vol 3 or the event out at the moment called Ultimatum, unless you like terrible stories. Instead pick up Ultimates vol 1 and vol 2. These two series are incredible and will blow your mind.
It really depends on what you like the look of and don't be intimidated by the number on the issues as each issue has a recap page and if you like it enough there are always the trades to buy previous story lines. However you are trying to grasp a general feel of the MU as a whole, I'd say pick up New Avengers. Generally it's been a good series but one of it's best qualities is that since issue #1, it has been leading the Marvel universe in terms of plot and tone for many years now.