Looking for a flat in Manchester

I'm looking for a flat near-ish the University of Manchester (ideally no more than a 30 - 40 minute commute by transit). I'm a grad student starting a PhD at the University of Manchester. I'm generally fairly quiet and mellow, reasonably tidy, and enjoy hiking, cycling, board games, and cooking. I'm especially interested in the Didsbury, Withington, and Chorlton neighborhoods, but generally care more about the specific flat, people I'm with, and transit time than the precise neighborhood. I'm part of the LGBTQ+ community, so having flatmates that are supportive / accepting is a must.