If humans ever moved to another planet in this solar-system, what constellations would the sun meet from that perspective? What constellations would the sun look like it is meeting from the perspective of Jupiter, for example?
The path of the sun would be very similar.
The positions of the stars are almost exactly the same. They are so far away that moving to Jupiter won't change their apparent position in any way that you could see (though it could be measured with a telescope)
All the planets move roughly in the same plane, called the ecliptic. This means that the path of the sun, as seen from any of the planets is also close to the ecliptic, and so the sun would move through the same parts of the sky.
From the perspective of Jupiter, for example, the Sun would travel through the same 13 constellations, but it would also just cross into the corner of Cetus for a few days, the next time being in 2028 (I'm using the IAU constellation boundaries). It would also move across the constellations much more slowly, taking 12 earth-years to complete a full lap (you can confirm this using Stellarium)
From the perspective of Mars, the motion of the sun would be along the same line, but it would move a lot faster when Mars is closer to the sun, due to Mars's elliptical orbit.
From Pluto, which doesn't orbit close to the plane of the ecliptic, the sun's path would be different and for (say) Halley's comet it would be completely different