The airport PI you are looking at is the one at Runger Lane, there is another one at Heald Green (right beside Heald Green station- the last station before the airport)-first train at 0541 for the 6 minute ride.
It is also on the #368 bus route from Stockport to the airport at 0518 and 0543.
So that would do for an 8am short haul or 9am longhaul flight.
Yes the Ibis Budget is 15 minutes walk from The Station, is next to T2, 20 minutes walk to T1, 25 to T3 (all conservative figures).
Personally I've used the Travelodge at Stockport (very central) and a fast motorway ride on the bus in about 20 minutes- buses from 0430. There is also a Holiday Inn Express up at Stockport Station- the station is now linked directly to the bus station. That would always be my first choice (but I am biased having known Stockport since I was knee high to a grasshopper).
So that will do for a 7am short haul/8am long haul flight.
Trains from Pic to the Airport start as early as 0340. The closest hotel is the Motel One (at the bottom of the approach road). I've not stayed there personally but have heard good things about the chain.
So that would suit a 6.30 am short haul/7.30 am long haul flight.