What is your intended purpose for this server?
If you plan on using WebDirect, you might not be able to get away with using a mac mini.
Else, from what I gather, there are still some mavericks issues being ironed out, so you might want to stick with 10.8. However I suspect that a 13.0v1 update will probably be coming out in the next few months.
Follow the guide that FM gives you for the rest:
Also, you will need some sort of backup solution since the mini only has a single drive (or did they cram two in there yet?)
We use minis quite a bit as servers over the past few years, and they've worked very well for us.
However, there are issues running FMS13 on the same mini with 10.9 OS Server. The new console doesn't work and you can't upload databases. There is a thread about this somewhere, but suffice to say, that if you want to run 10.9/FMS13 on a mini, don't install Server on that mini. I did a quick rebuild to resolve our problem and left Server off the rebuild. Everything else is working fine.
For light use, they will work. The built in hard drives are horribly slow unless you have a custom model with a fusioin or SSD drive. FMS13 is not certified for 10.9 Server, so stick with "plain" 10.9. Being that the memory and processor options are very limited, I would not recommend for WebDirect.
Thanks all, I'll stick with 10.8.