A Can of Worms

I just bought airplane tickets to London and back for myself and dresta11 ...for HLWW7. I'm getting quietly excited, and hopeful here *grins*.
I do have a question to all and sundry knowledgeable people on my f-list (and I am aware that it has been asked by others before, but I did not pay attention well enough *sheepish*): I assume the best way to get from London to Leeds is by train. Any suggestions on online booking? Also, I seem to recall that on a mailing list somehwere someone said something about a coach line straight from Heathrow to Leeds. Might there be any straight coach connections between Leeds and Gatwick or Leeds and Stansted airports? And if there are, would they be a better/cheaper choice that the train?
ETA: The airline company claims it takes appr. 45 minutes by airport coach from Stansted to central London. Would this apply also on a Friday around 13.30 - 14.00? What I am asking here is whether it is feasible to cath a train leaving 15.35 if the flight is supposed to come in at 13.00? Probably not or..? (No baggage claim time needed, but it seems still an awfully short timeframe?)
Any helpful comments are greatly appreciated:)