The Ibis on Bath Road isn't bad, I stayed there once. I like the Holiday Inn on Sipson Way (beware, there are 3 Holiday Inns in the area!) - this is one of the closest hotels to the airport, by the North gate. These are not as cheap as GBP19 I'm afraid.
As to getting back and forth, the Hotel Hoppa works but is slower and less frequent than the public buses and is ridiculously expensive at GBP4 each way. The local buses are free within 1 mile of the airport - look at this PDF map of the buses around Heathrow to work out which one to take, from T1/2/3 (or other maps for T4 or T5)
The local free buses are more frequent than the Hoppas until about 19:30, then they're about the same. Ah, if you need nightbuses, look for either buses with route numbers starting N like N9, or look on the map key for the buses with a 24hr schedule.