L visa. For staying for 2.5 months, you probably need a multiple entry L visa since the staying period of a single L visa is 30 days, 60 days for multiple entry visa.

Ms.Nikki, as Ms.Ling said, you need apply for L visa. However, you needn't a multiple entry L visa. The single entry L visa also can permit a 60 or 90 days stay duration in China. Please write your planned stay duration in China on the Visa Application Form, it is subject to the final decision of visa officials.
It takes 4 working days to process it. the fee is SGD 25 for single entry visa

Just to add another question: I have a friend (also Singapore citizen) who will be backpacking in China for 2.5 months. Will she need to produce evidence of hotel bookings -- will bookings for the first 3 days do? (And you mentioned it is up to the official how long a visa they wish to grant -- what are the criteria by which judge. And would it be possible to extend in China/ how much if if that's the case?

She needs to provide the proof of hotel booking. Perhaps she needs to apply for a double-entry visa which has a duration of stay of 60 days.