That's not entirely accurate. A lot of the intro decks from 2013 are splashed with another color.Intro decks from the core set are always one color where as intro decks from other sets are usually 2 colors.
Regardless, you can always find the decklists for pretty much any set just with a simple Google search. Event decks tend to be more competitive than Intro Decks, but also cost a bit more. Event decks go for $25 bucks, Intro Packs $15. Also, keep in mind that with the Intro pack you also get 2 booster packs included, whereas with the Event decks you don't.
M13 Intro Packs
M13 Event Decks
If you're looking to get back into the game, the biggest rules changes since you've last played are probably the 2010 rules changes and the addition of Planeswalkers (a new card type).
Other than those two things, the game hasn't changed much from a rules standpoint. These days creatures are generally a lot more powerful than they were back in the old days.