The Qantas safety record only applies to jets though, doesn't it? They've had a number of hull losses of propeller-based aircraft.
I believe Aer Lingus and Finnair have the same record, but perhaps sensibly don't boast too heavily about it.
As for airlines, Cathay is probably the best I've been on, but I haven't flown widely outside Europe. BA is great in Club, but can be a bit of a pain in pleb class on short-haul. Worst experience has to be Transavia, which would have made me long for Ryanair.