I did this a few years ago and followed the same course as Impulse9. However, I actually had a while between flights (and the check-in at Paddington was still open) so I checked in there and then walked around the city a bit before catching the tube (sans luggage) to Heathrow.

I think the choice between National Express and Standstead Express/Heathrow Express is based on time of day (the bus during rush hour can take forever), how much luggage you have (the bus involves less carrying of luggage and lots of luggage on the tube, especially during rush hour, can be a problem), and costs (the bus is likely cheaper).