Gatwick is the closest airport to Heathrow. And no, you're not missing something out of LHR... RyanAir and EasyJet and their ilk really have very few flights out of Heathrow. Mostly they operate out of Luton and Stansted. First of all, check out National Express
to see if you can catch a bus (coach) from Heathrow to either Gatwick, Luton or Stansted airport. That's going to be the easiest thing and I'm *pretty* sure they have coach service, but you may need to go into central London. If so, do this:
Check out National Express (or another coach company if you like, but I've had great luck with them) for tickets from any spot in Central London -- say, Hyde Park-- to any of the other three airports. After disembarking and going through customs at Heathrow, take the TUBE (Piccadilly line) into central London. It'll cost you approximately 7.50 GBP. Try to resist the allure of the "Heathrow Express" train into Liverpool Station if you're really on a budget. If you have an extra $20 or so to blow on transpo, go for it as it'll get you there a little quicker. But the tube should be fine. Catch your connecting bus to whichever airport at the designated spot. Victoria Coach Station is the main stop but there are pickup points around the city.
PM me if you need more specific information about this.