I recommend Aftermath, Morrow Project and Apocalypse World.
The 4th Edition Morrow Project book is a high quality product which benefits from updated info while retaining the system that made the original version great. You can also look for 3rd Edition Morrow Project on Ebay, which is probably much cheaper and is still a great game using the same rules. It is well supported with adventure supplements.
Aftermath is an old-school hardcore post-nuclear rules heavy game, but no more so than Pathfinder or D&D 3.5. It focuses on the 20 years after Mad Max type setting and has interesting rules for scavenging, custom armor, running small armies and other post-nuclear aspects beyond the immediate battle for survival. And for a $12 pdf on drivethrurpg, what the hey. I often use Morrow Project and Aftermath together, and oh, the adventures we had!
Apocalypse World focuses on the narrative aspects of a post-nuclear game and has an interesting tone.
Freedom Fighters, which is another old school game with a setting like Red Dawn.
I like Living Steel and Phoenix Command too. I converted Aftermath and Morrow Project to this system. Living Steel is a futuristic post-apocalypse setting, and Phoenix Command is its underlying game mechanics, which I found to be a really good tabletop small arms battle game. We would have three players each with a team of 6 soldiers, and the games would be over in an hour and a half.
http://rpg.drivethrustuff.com/...t/584/Aftermath?it=1
http://store.timelineltd.com/T...d-Hardback_p_21.html
http://rpg.drivethrustuff.com/...ilters=0_0_44825_0_0
It depends on the tastes of you and your players, and their willingness to learn a new system which won't be like what they're used to. Morrow Project is good for people new to the post-nuclear genre because it has good rules which are pretty simple to learn and play, and it places the characters in the role of good guys with a clear mission. Morrow Project, Aftermath and Living Steel/Phoenix Command are LETHAL game systems. I suggest having some practice battles before making characters the players care about.
For reading, I suggest:
Early Deathlands, like Pilgrimage to Hell, Homecoming and Neutron Solstice. Just bear in mind the books are very formulaic.
The Postman by David Brin
The Roadbuilders
A Canticle for Liebowitz
The Survivalist
Star Man's Son by Andre Norton
Some Will Not Die by Algis Budrys
Damnation Alley by Roger Zelazny