I bought one of the refurb minis for $469. It is very nice. It still isn't my primary machine yet. I picked it up so I could run ML for testing. Once that's done, I might just switch to the thing full time, especially since I put 8 GB of RAM in the thing. It runs nicely compared to the 4GB in my 2008 Macbook.
I wouldn't try to get by with an iPad and no computer of my own. Once I had my own computer, then I'd consider an iPad as my "road machine". There is a guy who uses an iPad as his main computer at ipadalone.com. It can be done but as much as I like my iPad, I still wouldn't recommend it as an "only" machine.
There really is no such thing as sync with a desktop any more. Well there is but it's no longer necessary now that there's iCloud. So I'd say go for the Mac mini first, get a $149 monitor, Apple KB (wired) and wired usb mouse. Then when you can afford it, get an iPad as your road machine.
hope this helps...