Hi,
I suggest you don't bother with fibre for connecting the PC's for various reasons.
1) users more likely to damage cable
2) you need to get networks cards for each PC with fible connectors or you get fibre to copper converters for each PC.
At end of day day depends on what your users are using PC's for, how quick network connections needs to be, etc etc. I also assume from your description that you only have one building ? If you need to go outside then you should use fibre to prevent lightning strikes.
You may find benefit in using fibre for your back up system because you may get higher transfer rates and therefore backup will be quicker. Again depends on how you are backing up, how many servers, how quick it has to be done, etc.
Come back if you have more questions, I have designed and installed fibre networks for companies.
Denis