Thanks to everyone's thoughtful replies. Very helpful, and it seems like flying back to Berlin is a no-brainer if I'm finishing in Budapest.
My travel dates of are arriving Berlin on Oct 7th, followed by Dresden, day trip to Görlitz, Prague, then Budapest. I have considered reverse engineering the second leg of my trip and flying Berlin to Budapest, then heading up to Prague and finishing in Dresden/Görlitz. Then a short and easy train ride to Berlin from Dresden on my final day. My only problem with revising my itinerary is that it forces me to hit Prague on a weekend, which I was hoping to avoid. My original itinerary is:
Arr Berlin Oct 7th for 7 nights
Arr Dresden Oct 14th for 2 nights
Arr Prague Oct 16 for 3 nights
Arr Budapest Oct 19-22/23 3-4 nights
Oct 23 fly back to USA from Berlin (TXL)
As far as the horror stories for the budget airlines, a simple search for reviews (such as Yelp) don't paint them in a positive light. I have no problem flying them, and mostly just wanted to know if people felt they were generally reliable and on-time.
Again, thanks for the replies and if there's any further suggestions it is appreciated.