Well if you want to get to AMS earlier your options are either:
- take BA's offer of the LHR flight, but you don't want to do that
- book the easyJet flight from LGW at 12.55 for approx £95 each. BA won't pay the cost of that, but I think you would get a small amount back for your cancelled flight to offset it. Not sure you want the hassle of dealing with that
As such, I'd guess your preferred option is to take the 16.00 flight BA have rebooked you on.
Deal with the compensation question later. If the cancellation isn't directly the result of weather, you may be entitled to it. Put in a claim when you get home and see. Don't bank on it though.