Regarding travel to and from the airports, I recently took public transit to/from Don Meuang Airport.

Landing in the morning, I hopped the A2 bus right at the terminal for 30 THB. It took the tollway and stopped at Central Ladprao, BTS Mor Chit, terminating at Victory Monument (where I took a bus to my destination).

On the way back, I took the BTS back to V.M. and waited in the same spot. I didn't see an A2, deciding to hop the 510 instead. A2, 29, and 510 all pass DMK. A2 goes right into the terminal and drops you curbside, 29 takes the surface streets, 510 takes the tollway, and both let you off on the street, right at the overhead walkway across from the airport (an overhead foot bridge and few hundred meters of walking required).
The fare for the 510 was 19 THB.