Personally, I did not find the experience of moving to Ukraine particularly stressful. I moved to Ukraine to be with my partner and daughter, so I was moving for personal reasons and I wanted to move.
I have been very lucky to meet a woman who has an amazing family. They have done everything possible to welcome me into their family and also into their country. They have helped and advised on almost every subject that you can imagine. I would say that this has been the biggest stress reduction element in the whole experience. I have not got stressed because I know I have the support of family.
I also spent over 2 years learning Russian, before I moved to Ukraine. It is hard to say, but this has enabled me to "get by" when I go to the supermarket or to a restaurant. I am not proficient at all, but I do my best. I don't know how much this reduces stress, but I'd say it helps a lot too. In my city, almost no-one speaks English, so I think it is critically important to know some of the language.
I would also advise anyone to indulge in the city and culture where they move. Do the tourist things and also the usual things. You'll get to meet new people and learn quickly what it is like to live there.