I wanted to get into reading comics and my first thought was to hit a comic book shop and look for 1st Issue Comic books? Is this the proper approach? I'm not a hardcore fanatic and the approach above seemed to make the most sense at the time.
The two heroes I would like to focus on are Batman and Spider-Man as they are the heroes I grew up to as a child.
If you want to start on origins of super heroes, a little bit of google digging is all you need; luckily for you, i know that a good batman origin comic is called 'Year One' look it up and see what you think!
Other than that, just find something you like the look of in a shop and buy the first in that series! An awesome series to get you on your way is called 'Civil War' - everyone who into Marvel comics know about it, coz it includes a bucket load of characters and has a great story to it, the only problem is you may need to spend some time with a Marvel wikipedia close at hand if you dont get any of the references!
Starting with one of these series might be good as well: World War Hulk, Astonishing Xmen, or Invincible Iron Man - they're some of the most popular marvel series.
Basically, pick a superhero, and ask the guy behind the comic book store counter where to start! Usually you can order comics into the store if they dont have what you're looking for.
I hope i helped and i wish you the best of luck in finding a series you really enjoy!!