I don't recommend reading OMIT it explains the details of OMD or at leasast what happed to make them not get married.

I've never really cared for Aunt May at all. I don't know why Marvel is so attached to the character. I liked Peter Parker when he was the teacher in the Marvel Knights series. I still want to see Aunt May just die from Mephisto with him saying "I'm the devil so ha ha ha" at the end of OMIT. Sorry to vent a little haha

I recently got back into Spidey titles.  After consulting my local comic shop and looking around this site, this is how I went about getting caught up. 
 
-"One More Day"- I got the trade paperback to make things easy.  This will get you up to date on the current status of Peter and Mary Jane and prepare you for OMIT
-Then I started with The Gauntlet storyline in Amazing#612.  With this story arc you get caught up with the current status of Electro, Rhino, Mysterio, Chameleon, Sandman and get set up for the Grim Hunt story arc.
 
It seems to me that you picked a great time to get back into the Spidey-verse.  I've enjoyed Gauntlet and Grim Hunt immensely.

If you want to understand origin of species you'll have to read the American Son Arch 595 to 599 I believe and parts of that arc redefine wrong personally I HATE O.M.I.T it adds insult to injury I'm not going to get into it here if you want to know more read my review of the 1st 2 parts of the arc

start at the gauntlet it 's not too far behind and it's good !!!!