Thanks all for advice. The story is, we want to get to village for the big Easter holiday. Almost everything is sold out. I guess millions of Ukrainians travel on these days.
However, my companion was able to find train tickets for one day early: that is, Thursday. The overnight ride in a regular train car will not be comfortable (not my American idea of comfortable!) But anyway, the tickets are dirt cheap.
On the express, If you want comfort and privacy, go on 1st class for a little more. It will be worth it. If you found yourself on communal train, the one that goes slow and stop everywhere, it will be best to keep a low profile and secure all your belongings. Is spring break over there, so Wear sunglasses to avoid conflict/ haracter.