If I were you I'd check out LH
and connect on to Krakow. If you fly LH
the whole way you'll get miles you could eventually transfer to any of the Star Alliance Carriers (more options then any other alliance out there) and if you eventually change your opinion on LOT and use them, they are now part of Star as well.
You could also take UA
and LOT or you could take UA
and connect on LOT etc etc. Star Alliance is the only way to go for the global business traveller! As a million mile flier myself, I've come to love the Star Alliance.
(Granted I work for a Star Carrier so I'm biased). Nothing like 600,000 employees worldwide looking after you! With service to over 700 destinations around the world, those miles you start accumulating will get you further then any other alliance!
The debate continues... Starwood or Hyatt... which is better