Challenges do have an impact on later runs. Some more than others.

I wouldn’t worry too much about order; do whichever ones strike you as fun. If you play a lot then you will end up doing many challenges; I am on 20 each of energy, black sky, pacifism; 10 anarchy, 8 winter, 5 atheism, 1 1000-years. (Atheism is slow.) But I think you should leave strategizing about challenges for later. They’re all worth doing once; as you do them, see how much fun (if any) you have and how much (if at all) you value what they give you, and then just do whichever ones you feel like. The ones I’ve done 20x each are (I think) the most helpful for long runs (other than 1000 Years, which you should do as soon as you’ve been able to get 1000ish time crystals because it will make building up TCs/relics easier).

But, for what it’s worth, my suggestions: Maybe do Winter first because it’s easy and it’s nice never to have to think “wait, do I have enough catnip production even if I’m hit by a cold winter?”. (You still have to worry about winter itself, but those predictably come around once a year so you can just look and see whether you have enough without having to wait a long time, whereas cold winters are less frequent.) Do 1000 Years as soon as you’ve got 1000 time crystals. Do at least one Anarchy early so you accumulate karma faster. Do at least one Atheism early; it makes a substantial difference to production (once you’ve got Solar Rev in any given run). Do everything else as you feel like it.

I haven’t bothered with Iron Will or with Post Apocalypse (which I think you won’t have available for ages anyway).