Thank you, FindAWay!

We are pretty flexible with the airline choice and are happy to consider other options, but I guess I should have said that Lufthansa and United are the only reasonably priced airlines with convenient connections and large bassinets.

I personally like both Swiss and British Airways (had good experience with them in the past). Unfortunately, BA are about $2000 more expensive (in total) than Lufthansa or United, and their connections are far less convenient. In turn, Swiss bassinets are for babies up to 8 months only, so we won't be able to use one.

As for Austrian or LOT, we'll have to make at least two connections with them (vs. one with Lufthansa or United), while we definitely prefer having one connection.