I think your priorities are backwards; it sounds like you're going to decide how to spend your time based on which computer you buy. First decide whether or not you're going to do those things, then decide which computer can do it. Personally, I don't like the bundled display aspect of iMacs, but if I was frequently doing heavy video/photo editing, I wouldn't use a mini when faster options are available.
thanks for this comment, it pretty much changed my mind to consider the iMac. I ended up going with a refurbished 2.53ghz Mac Mini. I think it should be good enough for my secondary, home computing needs. I'll be replacing my current MacBook Pro sometime later this year (I like to sell my laptop before my 3 year applecare is up) so I'll have a pretty strong computer there too.