Title says it all. I do prefer "Marvel Now", but I will accept some of the older Avengers series. I've heard of "New Avengers" and the "Civil War" series were those any good? I've been slowly and heavily going to DC, I love Iron Man (favorite) but his art is probably (in my opinion) the worst of any super hero. So please revive my faith in Marvel :D
If you like Marvel Now stuff then I'd personally suggest getting Indestructible Hulk and Thor: God of Thunder. Both have had good artists (Lenil Yu for Hulk and Esad Ribik for Thor*). Both titles should be pretty easy to get up to speed with, though if money allows I'd get all the issues back to number 1 (they haven't been around very long.)
Uncanny Avengers is also really good, but for that I definitely recommend starting from the first issue, again there aren't that many issues yet.
As for Civil War I liked it but at this point it isn't necessary for getting up to speed on things. If you don't like to chance it on the new stuff then message me back and I can recommend some trades.
*When they get subbed out it's usually for someone good like Walt Simonson.
Right now marvel is having a sale on its Sacrlet spiderman issues 1-12 for .99 each issues that's my recommendation for the marvel now. It's very underrated and its a darn shame it's getting canceled. For other series I suggest Avengers vol 4 which is right after ur dark reign it's one of my fav avengers series. New avenger and mighty avengers are both great series that took place around the times of the civil war which made me respect both luck cage and hank pym on each teams.
I would say Nova, Venom and All New X-Men. You will have to go digging around if you wanna get the whole story in Venom and All New X-Men is FAR back...you'd have to start all the way to Road To Schism and thereafter. If you can get your hands on the 16 issue series of The Punisher and the limited series after you're in for a real treat. Skip Punisher : Nightmare though....you'll thank me but DEFINITELY get Punisher : Warzone.
From Marvel Now the best titles have been Guardians of the Galaxy (first trade just released, big stuff happening now with Neil Gaiman's character Angela) and Hawkeye (two trades out by now, plus you can jump on at any time--they make it simple and fantastic like that). New Avengers volume 1 Everything Dies is brilliant. I haven't been reading Thor or Hulk but they've been getting good reviews. And the Avengers title has been huge leading up to Infinity.
Jumping back a few years, I've got to recommend Joss Whedon's 24-issue run on Astonishing X-Men. If you like the Iron Man movies there's the Extremis trade collection which inspires a bit of movie plot. If you like Spider-Man then Ends of the Earth was great as was Carnage USA.
See if your comic shop still has chapters one, two and three of the X-Men's Battle of the Atom crossover event, which is shaping up to be awesome too and started last week.
As for Uncanny Avengers, I can't stand the writer, Rick Remender, so wouldn't go near that title at all. But every author has their fans and not-fans.