Way to Ukraine

Regarding transportation, I highly recommend taking a train from Poland. There are many affordable options available, and this route is both convenient and comfortable.

Direct trains to Kyiv are available from Przemysl and Chelm, tickets at booking.uz.gov.ua, and appear 20 days before departure day (I recommend buying them ASAP because the number of places is limited). There’s also a direct train from Warsaw but it’s virtually impossible to get tickets. Chelm is also a more convenient one because you pass the boarding control in the train while in Prsemysl you should go through the special building at the train station.

From Warsaw to Kyiv:

11:53 departure from Warsaw to Chelm (local train, tickets at bilkom.pl)
15:07 arriving to Chelm
16:35 departure from Chelm (international night train, about $40 per ticket, 1st class)
06:30 (+1) arriving to Kyiv

or:
17:49 departure from Warsaw to Chelm (local train)
21:10 arriving to Chelm
23:40 departure from Chelm (international night train, about $40 per ticket, 1st class)
13:07 (+1) arriving to Kyiv

From Krakow to Kyiv:

16:03 departure from Krakow to Przemysl (local train, tickets at bilkom.pl)
19:44 arriving to Przemysl
20:28 departure from Przemysl (international night train, about $55 per ticket, 1st class)
09:03 (+1) arriving to Kyiv

There are 4 trains from Prsemysl to Kyiv, two of them are night ones and two are Intercity with seats only, not suitable for sleeping.