The European legacy carriers seem to have most things sussed as far as their websites are concerned. I've never had any problems when booking through BA, KLM, Air France, SAS, etc.
Aeroflot's website deserves a special mention, purely because it lists tail numbers of the aircraft that actually operated (or is operating) a given flight.
EasyJet appear to be a front-runner in the LCC stakes. All the info you need is right there at your fingertips.
The Ryanair site, on the other hand, leaves a lot to be desired but I guess that when you're paying peanuts for a flight, you don't expect much of what the company does to be up-to-scratch.....
Overall, my choice would be www.ba.com. It ticks all the boxes.
Vidi, Vici, Veni. I saw, I conquered, I came.