you didn't say which state you are going to ....... anyhowly most european carriers have more flights to most states in the US like BA,KLM and even KQ through their partners.....
There are many things you ought to consider....cheap is sometimes expensive...
1) Will you need to change your travel plans after you have paid for your ticket and it so can this be done and at what fee ?
2) After check on the airlines websites ( KLM,SWISS,SN,BA,KQ or Virgin) and see who has the best prices with the best conditions......
3) If you still have time visit some 2 or 3 major travel agents ...they tend to be much better and can quite easily cope with any problems you may encounter on your travel.... ( HRG-Elite travel,Bunson or Uniglobe are very good.