Fallowfield
Fallowfield is a student area. That is not a criticism, it is just what it is. The majority of the housing stock is HMOs, shared Victorian terrace houses, and most of the tenants are undergraduates from the University of Manchester and MMU. The high street has budget takeaways, pubs, and late-night venues. Platt Fields Park, which has a large lake and a skate park, is the main green space.
If you are a student who wants to be in the middle of that environment, close to campus and living cheaply, Fallowfield makes obvious sense. If you are not a student, or you are a postgraduate who wants a quieter base, it probably does not.
The Wilmslow Road corridor, which runs through Fallowfield, has long been claimed as one of the busiest bus corridors in Europe. Whether or not that is technically verifiable, the bus frequency is genuinely high and services run directly to both universities and into the city centre throughout the day.
On rent: rooms in shared houses typically run from £500 to £700 per month excluding bills. One-bedroom flats are less common but come up at around £750 to £900 per month. It is the cheapest of the three areas on a per-person basis.