I know a guy who had a business like that about 12 years ago, I spent a lot of time there and learned a lot about running the whole thing.

Here are some problems you may face:
-People may use it as a place to run scam or blackmail operations.
-If you allow them to install whatever they like, it will most likely be pirated software and trojans.
-You have to calculate the cost of daily cleaning your computers. You'll quickly learn that people rarely wash their hands or turn away from the screen when sneezing.