BA sale now on. I use all sorts of things:
Jack's Flight club is a great heads up (notified me of BA sale before it was actually on the BA website!).
I use Skyscanner (although find the click throughs often different to what quoted on Skyscanner, so quite frustrating).
The last few years to the US, we've found BA to be the most competitive (although the deals haven't been as good this year). You need to check a variety of airports if possible. Also consider a fly-drive or fly-hotel package as they can often have great deals.
I've this morning booked for the 4 of us to go to New York next Easter holidays (we're flying across 2 weeks, but nearer the time will try to find some cheap domestic flights to go somewhere else) with BA for £1300. Had some Avios to cash in, so paid less than £1k. Bargain!
I've got no problems with BA, they've always served us very well.