Most of the posts above give the relevant information so all I will add is that I have flown easyJet many times and they have been fine in all aspects but are a typical LCC. BA or LH are not going to be much different in service and certainly no safer, EZY are probably more punctual though and probably cheaper.

Gatwick is a better airport than either Luton or Stansted for passenger experience and EZY exclusively use Gatwick North terminal.

Good luck.