Actually, the distance doesn't do weird things. If you traveled at slow speeds (up to like several thousand kilometers per second) time dilation and length contraction would still be negligible and your timing of how long the journey took would mostly line up with someone on Earth.

But if you're traveling a significant fraction of the speed of light those effects become non-negligible. That's where our normal understanding of a universal notion of objective time and distance breaks down.

The equations of special relativity are actually very approachable if you know algebra, you should play around with them and plug in some numbers!

Another great example of both scale and speed. Even the near stars are far.