I'm still 'new' to Twilight: 2000, but I started with v1, so I've staked my claim that way. I've played a bit of Savage Worlds, and I think it could definitely work for this king of setting/story.
Another system I've been itching to try is FLOW, from the official
STALKER game (and I'm talking Roadside Picnic, not the video games). It's diceless, and is based on utilizing character skill and common sense to convince the GM that your idea will work, or maybe work half-way, etc etc. Character creation is also easy, and you can probably shoe-horn some stuff in for radiation and the like if you want to go full T2k.
I bought it last year during a sale, but have not had a chance to run it.