I wrote a chunk of D20 Apocalypse, I own most of the Darwins World books published to date, and I've run a few post apocalyptic games, so hopefully my advice will be helpful to you.
First, now that there are quality alternatives, I don't mind admitting that I have issues with D20 Modern. The philosophy behind the game design was sound, but actually using the system to make characters and NPCs is even more of a chore than making 3.5 characters. Regardless of how fond I am of Atomic Sunrise (which is really a quickly reinvented Gamma World for D20 Apocalypse), I think Darwin's World is the best prepackaged PA setting.
Your best choices for your rules system are either True20 or Modern20. Neither of those will give you the kind of headaches for making characters that D20 Modern will. True20 does away with the 3 - 18 ability stats and just uses the ability modifier. The skill system is streamlined, and hit points are replaced with a toughness save. I've run True20 Darwin's World and it was great. Every shot had the potential to be lethal, and that made things seem more grim and gritty. The unfortunate part is that the only True20 product they did for DW was the player's guide, which means that if you go that route, you'll be doing a lot of converting.
My other recommendation is Modern20. This system is closer in nature to D20 Modern, but the classes are not generic and the levels run 1 - 20. If you didn't mind having the D20 Modern book handy while you're running games, this system is similar enough to Modern that you could easily convert all existing DW material over to it and run adventures straight out of the book. I don't see any reason that you couldn't use the advanced classes from the DW player's book with it, modifying prerequisites as needed.
Either way, I'd definitely go with Darwin's World. I have Gama World D20 and while it's not bad per se, it's not as good as DW. DW has a lot of support out there for it and from my understanding, they have no intention of stopping support for it at any time in the future. The material is well written, and the core books provide tons and tons of material such as organizations, PA equipment, setting, and mutant creatures. As far as I'm concerned, it is the definitive PA game.
Have fun with this. I'll be breaking out the DW stuff myself soon to write an adventure for it.