What Thunderbird would most likely survive an apocalypse?
I would say that very much depends on what type of apocalypse. If it's the sun exploding then I don't think any of them would survive. If it was a zombie apocalypse then I think they would all survive, mostly because I don't think zombie bites would do anything to vehicles.
If we're talking about which Thunderbird would be best in aiding your own survival then I think it's a little more complicated. Again it depends on the type of apocalypse. But I would have to choose Thunderbird 5. It's designed to be somewhere you could live for a long time so has all the resources you would need already on board. Also, by orbiting the Earth you'd most likely avoid any danger entirely.
Thunderbird 3 is a similar story. It is designed with living areas in order to support the pilots during deep space journeys, and it's ability to travel into space would also keep you safe from any dangers on Earth. Additionally, with Maximum MAX, it would have some defence against any dangers it might face.
Thunderbirds 4 and Shadow, whilst they would have their benefits in an apocalypse, are a lot smaller in size and therefore don't have the same benefits in supporting life long term. Although I suppose you could live in Thunderbird 4 at the bottom of the ocean for a little while to evade any danger.
Thunderbirds 1 and 2 fall somewhere in the middle. Both are capable of storing equipment that would aid in an apocalypse, and are large enough to provide comfortable living space (especially TB2), even if they weren't designed with that in mind.
I hope this answers your question? Although it is difficult to answer as there are many different types of apocalypse.