There are a number of budget airlines that have acquired new generation, more efficient airplanes than the big legacy airlines like American, Delta and United airlines have. They have entered the transatlantic market the last 3 years.
We flew Norwegian Air Shuttle from Budapest to Boston last April for $238. In April, we are flying Dublin to Newburg, NY for $158. I got a note yesterday the Dublin flight is going to be on a brand new Boeing 737 Max which is a stretch 737 with extended range. Most of their other flights are on Boeing 787s.
Economy airlines are no frills and I have no problem picnicing--bringing my own food on board. But the budget airlines have allowed us to take twice as many European vacations as we usually would take.
Don't think Turkish Airlines is a second tier airline as they are a very good operation. Trouble is their return flights sometimes require staying overnight in Istanbul.
And as far as getting a Eurail Pass, experienced travelers usually book train reservations ahead of time and travel much cheaper than the Eurail Pass.