My PC has broken, if I buy a Mac, can I transfer my entire library over with ease?

That depends. What is broken on the PC? If the hard drive has failed and you do not have a backup, you will need to look into data recovery services.

It's easy to move stuff over from a working PC. One that is not functioning is a bit more difficult.

Take a look at this Apple article about data migration from a PC, it may be useful.

Best of luck.