It will be definitely cheaper to travel via Ukraine + the route is much more straight.
Best way is to go via Chernivtsi, from there you can easily catch multiple trains to Lviv or even one till Kovel. But the only problem is Suceava-Chernivtsi connection, after the flood train #59/60 is not running anymore, so the only choice there buses. But as far we heard bus connection is problematic there as well. Officially there is only one bus per day - early morning from Chernivtsi and in the afternoon from Suceava (cost around 4-5 euro). And there were rumors about some half-official minibuses, but it's better to search/ask for those already in Suceava.
Train №668 Chernivtsi-Kovel leaves at 15:21, arrives to Kovel at 5:20am, "kupe" - 90 UAH, "platskartny" - 62 UAH. From Kovel there are multiple buses to Poland (Chelm, Lublin, Warsawa). For fares and timetable for polish trains -
http://rozklad-pkp.pl/If not via Kovel, then you might think of going via Lviv (train #604 20:35-7:41, train #142 22:20-4:00), 'kupe' - 72 UAH, "platskartny" - 52 UAH. From Lviv you can either go directly to Warsaw by bus (daytime and overnight buses, ticket around 210 UAH) or go via Medyka-Przemysl and afterward by train.
Other option is to go from Suceava to Sighetu Marmatiei, cross the border to Ukrainian Solotvino and board overnight train to Lviv (departs Solotvino at 15:33, arrives at 6:40am, 'kupe' - 81 UAH, "platskartny" - 57 UAH) or go by bus to Muckachevo (multiple trains to Lviv from there)
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