All this soul searching for an overnight between flights
? Coming into the city then going back out the next morning will take up somewhere between 2 and 3 hours of your down time and cost you money and a fair bit of messing about. Fine if there's something you want to do in town, but otherwise it sounds like wasting time and money.
If you are happy with the 70-odd quid, the Hilton sounds the sensible option: the on-campus Radisson even better if you have oodles of the right sort of points.
Save money but sacrifice time and accept a bit of faff, and you have Stockport and a free breakfast.
Manchester Hilton isn't in the most attractive area of the city, but it's minutes away from an airport tram stop and Deansgate railway station, with limited services to the airport, passing through Piccadilly.
Indigo is between Victoria Station and the football museum and an entertainment district (but not a very attractive one). Victoria has regular trains to the airport, passing through Piccadilly.
DoubleTree is between Piccadilly Station and Manchester's gay village. Piccadilly has the best airport connection - as you might have gathered.
Sadly the train schedules get messed up, so although it's a frequent service, be aware it can go wrong. The tram is OK, but seems to stop at every street corner and takes ages: well, about 50 minutes.
Uber's around £25: easy from the city but a bit of a trial finding pick-up spots a the airport. The airport itself is a mess.