I will need mail but not many accounts, just the normal firstname.lastname@example.org etc.
Only experience I have with DNs is updating the DNs on my domain names.
I also have a time capsule which I use at the moment for wifi and backing up our two MacBooks. So I've vaguely used time machine to set these up
OK, great. Yeah, I'd say you're in a good position to make the transition. The reason I ask about TimeMachine is because the MacMini server comes with two drives, which is perfect for creating a TimeMachine backup of your server.
I will throw one important bit of advice out: Buy this book... http://shop.oreilly.com/product/9780596100575.do One of the biggest gotchas of OS X Server administration, neh, server administration, is understanding and working with DNS. This book is considered the bible of DNS and will really put you in a position to be knowledgable and successful at administration.
Personally I wouldn't commit to such a plan with zero experience in OS X Server. While Apple likes to make it sounds like Server is a no brainer it's far from it. You still have to understand the issues associated with running a server and all of the underlying technologies that support it, affect it and work alongside it. You'd be surprised how much your current host is protecting you from.
At a minimum I would buy OS X Server from the App Store and give it a run through using another domain or sub-domain and see how you go.