Congrats on the mini! I have one and I think it's the best computer I've ever owned.
I love to read, so I have several apps for reading that I can recommend it's iBooks (for ebooks and PDFs, also has a store built-in), Blogshelf II (RSS reader similar to iBooks in design), Zite (was mentioned above, great app) and Manga Meow (if you like Japanese comics). I read couple of great free magazines Distro (on gadgets), Cineworld (cinema), Snap (that's for Hipstamatic fans), TRVL (travels). I also subscribed for tech. magazine, which is nice, although I like free Distro better.
Tapatalk of course is a must.
I am a photography lover, and my primary camera is my iPhone, but I also use my mini to take pictures fairly often. My favorite apps for photography and editing are Camera+, Hipstamatic, ClassicTOY, iSupr8, MiniatureCam, Snapseed, and of course Instagram and Oggl.
Also, I'd suggest you get either AppPriceDrop app or find the website AppShopper and create shortcut icon to it (they have an app but I don't like it I couldn't figure out how it works, it showed me a couple of apps a day only. I also don't understand why such an app has to be social). These are to monitor discounts for apps you want or discover apps.