Well, this is what I've found:
Vilnius-Minsk - 6 trains a day, some starting from Kalingrad:
about 10-15USD single, check www.litrail.lt
for information, available in Lithuanian, English and Russian
Minsk-Kiev - 2 direct trains at 1231-0003 (journey planners will indicate a connection as well using this train, but will save only 1 minute for the journey time) and 2125-0743, 1 connection - 00:50-04:27 connect via Jlobin 06:25-13:42, about 12USD single
Kiev-Chisinau - 2 trains a day direct 0755-2259 and 0355-1700, 1 connection 1331-0552 via Shmerinka, approx 30GBP
Chisinau-Bucharest - 1 connection overnight 1730-0657 approx £22, buses may be faster and more frequent. This train also comes up as a connecting service that will arrive into Bucharest about 20 minutes earlier.
From what I understand, it would be cheaper to book these tickets when you get there, although you can book most through RealRussia, or possibly DB? Buses may also be more frequent, and cheaper. Check hafas.bene-system.com/bin/query.exe/en?L=b-rail&