I just moved to Leeds from Belfast, and ended up making two house-hunting trips. After the places I've seen, I would never recommend renting someplace without seeing it first. Pictures do NOT tell you everything!
Agents tend to be a bit geographically specific. I'm near the University of Leeds, and am happy to recommend our agent, Central Properties. Others that seemed to deal in decent professional-type properties and seemed to be reputable and organized were Redbrick, Morgans City Living, and William H. Brown. David Moor is huge and has loads of properties, but every one we looked at was nasty, and I wasn't impressed with the agent we worked with.
Feel free to ask more questions or PM me!