What airline should I fly from Los Angeles to Budapest?

If it was my trip I'd choose Austrian airlines. Vienna is a comparatively small airport so a transfer there will be a much smoother experience.

I have flown Turkish Air to Budapest maybe 20 times over the years and granted, changing in Istanbul it a tad out of the way and it probably adds an hour to the airtime vs changing in Frankfurt; but I love their service, efficiency, lack of canceled and late flights and changing in IST is a breeze (despite its size).

Cost? Ehhhh, competitive, but not always the cheapest.

I will be back on them in June.

You can also use Turkish Air as an excuse to see a place you hadn't thought of, as no other airline flies to more destinations and sometimes multi-city and open jaw flights with them can be the same cost or less expensive than a straight RT flight.

In past years I have flown to Kyiv, spent a few days, then take Wizzair to Budapest and home on Turkish Air from Budapest; even counting the Wizzair flight the Turkish Air Open Jaw was cheaper than a Turkish Air RT to Budapest (have done this a lot to places like Sarajevo and Podgorica).

But I have flown all the major carriers there, and they are all "serviceable"; and if you do choose Austrian, layover in Vienna for a day or two and take the train to Budapest.

I got curious and looked, on Turkish Air from LA you would have a 1 hour layover in IST. I have done a 1 hour layover, actually twice. It can be done, but .................. naaaaa, not if you can find something else. Coming back, it is also a 1 hour layover. Coming back I wouldn't risk it because from time to time you have to go through security again. But I did do it one time and I only risked it because there is a hotel near the gate and a flight early the next morning.

I fly from SFO and have used United, which partners with Lufthansa. I am usually able to get my desired 2-3 hr connection through Frankfurt or Munich--starts with United, ends with Lufthansa--and have had no issues on the 5 trips I've made.

I've flown both KLM(Delta) and Lufthansa(United), because of loyalty programs, and both are fine.

Are you familiar with long-haul travel and will you be seated in regular economy seating? My preference is to check the aircraft type and review the seating configuration and availability. Also check the number of stops: can you make the trip with just one stop, or is two required? I also think it's important to check your entry into Europe. I like to fly into AMS or MUC. I try to avoid CDG. I've never had a bad experience there, it's just not my favorite.

In terms of service, I think you'll find most major airlines are pretty similar.

I live in Pest and have flown Turkish (half-dozen times?), KLM/Air France (maybe 10 trips) and Lufthansa (once). All are fine. I second what James said about Turkish but I seem to get either very short or very long connections with them - they were closing the doors once and I just made the flight. Amsterdam is nice because if passport control lines are long, they'll scoot you on your way.