From Luton central train station/bus station ground is 15 minute walk.
You don't really want to be at the Airport train station or bus station as a lot further from ground. If your bus drops you at Airport bus station do not get a taxi from there robbing bastards will cost you twenty quid for five minute journey.
If for whatever reason your bus drops you at airport. Walk out of the airport down the hill and ring a cab outside Ibis hotel.
01582 404040 is fair priced taxi firm, also they confirm booking via texts.
Regarding arriving at Milton Keynes train station and then getting bus to Luton, my view not ideal as MK train station a long way 15-20minutes from M1, then a further 30minutes at least to Luton. You would just be better off getting bus/coach Cov to Luton as would pobably be quicker and cheaper.
If you drive down in a car your looking at an hour. The earlier you get down the closer you will be able to park on the side streets near the ground.