Stretford is very mixed but a bit far from the university. Whalley Range is closer and again is mixed, the chorlton side tends to be a lot posher/nicer than the moss side end. Hulme is an old hell hole but the regeneration has made huge improvements and is now very popular with students due to its walking distance to all three universities (Manc, MMU and Salford). Old Trafford is mixed it depends which end, most of it like stretford offers little to students.
You don't want to live in trafford park unless you have a fettish for industrial estates (once the biggest in the world).
Personaly I would be looking at:-
Chorlton - Very bohemian, lots of real ale pubs, organic supermarkets and general oddness but I love the place.
Didsbury - Clone town but quite a leafy area with many bars.
Fallowfield - Not one of the nicest parts of Manchester but it is where most students live and has very good student bars and buses into town every second.
Hulme - If you can find some where new and cheap on the city centre end you can get a bargain and you can always walk to the city centre bars and pubs.
Whalley Range - The chorlton end is just an extension of Chorlton these days and has some good quality homes at good prices. The Alexandra Road end has a poorer bus service, but the upper chorlton road end is served by the frequent 86.
Stretford - The chorlton end is not too bad and is very close to the metrolink but not much there. The middle part is a bit rough and the Urmston part is too far though on a direct route to university (15).
Withington - Slap bang in the middle of Fallowfield and Didsbury, its becoming more popular with students. It is cheaper than Fallowfield in terms of rent and has better quality housing.
City Centre - Slightly more expensive and noisy but its not stupidly expensive due to a flood of apartments.