Calling Fallout Equestria Fans
If you're not already familiar with it, I suggest Coriolis. The system is quite simple and easily hackable, and being a spacefaring game it includes radiation rules that are pretty straightforward and manageable.
The authors also have a post-apocalyptic game based on the same system, Mutant, that may need little to no hacking for F:E, but I'm not familiar with that one specifically.
There are free quickstarts for both games, if you want to check them out. If I remember correctly the one for Mutant comes in 2 separate parts, though.