I have been trying to get into using my iPad for coaching, I've got as far as turning my training plans into PDF's and putting them on there. Also working on formulating a spreadsheet to keep score on there.
You can review the video straight away on the standard photo's app. You can also download iMovie, which is the video editing software. I have only used this on my Mac so not sure how it works on an iPad yet. But you can cut stuff out and edit it, Slow it down etc. I'd say the iPad mini would be good as its small and lightweight, but it doesn't have as good a battery as the iPad 4. The retina display on the big iPad (4) would be good for viewing the video back. I'd go for a large capacity one, pictures and video will soon fill up a 16GB. I'd also buy the 3G enabled one so you are always connected where ever you go.
I had a BlackBerry PlayBook, it was alright, but you wouldn't have the software capabilities of the iPad. Also, compared to my iPad 2 the BB PB was so laggy, and sometimes just refused to work.
Also, I don't find the lack of flash a problem. Apple are such a big driving force in technology that websites are moving to accommodate non flash devices