I recommend GeChic 1303H as a portable monitor
I've used GeChic 1303H for my mac air; I didn't get mine from Amazon though, I purchased directly from their website:
www.icitouchtech.com. I've only used it for a week with my Macbook Pro so I can't comment too much as of yet. It comes with an HDMI cable so you can hook it up to your mac mini as well.
I've listed some of the highlights of the monitor below:
- Great picture quality/resolution; I've only tried web browsing with the mac air and PS4 games so far but the monitor displays an an awesome 1080p picture with a clean refresh rate. Great colour range as well. You can make the picture very vibrant if needed.
- Easy to set up and use; can theoretically plug any device with visual output into this thing if you have the right adaptors/cables.
- Thin and light; this monitor is as thin as an iPhone 4
- Useful case/stand
- Simple menu navigation for settings