Looking for a 1-bed Flat with a Yard

I'm headed to Manchester this year as a Visiting PhD scholar at UoM. I'm looking to rent a quiet apartment (on a PGR budget) for myself and my 3 cats. I'd like to have a yard or park behind the apartment for my cats to access, and ideally I'd love a furnished place, though I'm more flexible on that. I'm tidy and great at communication, so if there's a flood or damage to the building I will always be in touch early to protect the property.

While I'm technically a student, I'm 35 and fall more accurately into the "professional" category. I worked in direct service for almost ten years and am now transitioning to a career in art history. I can offer two local references to my character and a reference from my current landlord as well.