Might be cheapest to go through LHR, I would assume the cheapest trans-Atlantic flights go through London?

Then jump on a Ryanair flight from STN. If you don't want to stay in London, tou could get the tube to Liverpool St and jump on a Terravision bus out to STN. Total cost one-way LHR-STN within London would be around £10.

Else: check Lufthansa, LOT, Finnair, Czech... They all fly to RIX.