My wife and I will be traveling from Berlin to Budapest the afternoon of May 4 (Saturday). I assume a non-stop flight isn't an issue; but would like some specific recommendations on what airlines are reliable and a good value. So long as there is public transportation from Berlin to the airport (which airport?) and from the Budapest airport to the city, our window of time for the flight could be anytime departing Berlin 14:00-16:00, and arriving Budapest 18:00 or a few hours earlier.
Bus 200E goes from airport terminal 2 to a major metro stop in Budapest, from there you can get anywhere. Looks like AirBerlin and EasyJet are the budget carriers making that trip, both go from Tegel, which is easy to get to (direct bus to/from Tegel and Beriln Hauptbahnhof). I haven't flown either airline so I can't give any advice, I'd just go with whatever is cheapest. Btw, I haven't flown this route, I was able to look up the info in less than 3 minutes using two google searches - "budapest airport public transit" and "berlin to budapest flight schedule". Just sayin.
You'd want to fly out of Berlin Tegel Airport on Air Berlin to Budapest. They're the second largest airline in Germany and #6 in riders in Europe.
Tegel is the main Berlin airport until their new consolidated airport is completed. EasyJet flies out of Berlin Schoenefeld airport. EasyJet is probably the best of the big budget European air carriers. You'd be okay on either. Compare prices online to see if either is much less than the other.