Advice from the 2009 Mac Mini manual:
If you’ll be away from your Mac mini for less than a few days, put it to sleep. When your Mac mini is in sleep, the display’s screen is dark. You can quickly wake your Mac mini and bypass the startup process.
In sleep mode the Mini uses very little electricity; even when switched off it still consumes a trickle, unless you unplug it from the mains. There is no really significant benefit in turning it off. Indeed it can be argued that it is beneficial for electrical components to be left powered up as it minimises thermal expansion and contraction. Overall though, probably not a lot in it one way or the other for consumer level devices.
My early 2009 Mini has been powered up almost 24/7 (unless I've been away for more than a few days) since I got it, timed to go into sleep mode after 20 minutes of non use (preferences > energy saver). It still has the original HDD.
I did shut down my 2005 original every evening. Anecdotal, I know, but the HDD and the power supply failed after a little over 4 years.
In the end, there's probably not much in it; up to you.