With international flights, you are going to have a lot more options going to Riga than to Kaunas or Vilnius, and in any case you are not going to have a massive number of different airlines to choose from.
Direct flights are pretty much out, so you will need to change in one of the bigger European hubs, or maybe Scandinavia or Warsaw. If you are changing flight in the UK then you might also find some flights to Palanga (which is the airport next to Klaipeda).