The rental shoes aren't bad at all tbh. Cleats would be at least that much, but remember you won't have the pedals to fit them correctly. As it's a one-off I'd just say rent
Depends on where you're riding. Unless replaced during the refurb the Manchester ones are many years old and have seen lots of feet! The cleats are replaced frequently though.
That's useful, thanks! I'll maybe try to get some Keo cleats then.