I'm with the crowd on this one, even being a Mini owner. The Mini is designed as a low price point machine that makes it easy for people to switch over to a Mac. I bought mine specifically for that reason, and I just plugged it into my Dell Keyboard, Display, and mouse. I figured i'd try it out and see what I thought. I'm sold. Little by little now, i've been replacing my hardware with Apple products. Keyboard...mouse...(but i'll wind up with a Macbook before a new display).
If you want to ease your feet into the Mac world without spending a lot of money, and you have a decent display handy, the mini may be a good choice if you have an external hard drive handy as well. But If you want lots of hard drive space and will rely solely on your computer, the Mini isn't the best machine for it. Mine has an 80GB drive, which would be a feat to fill up with images. But video can fill up a small drive like that quickly, especially full length movies. I get around this with a large external drive.
The iMacs are nicer machines in general. The 1.83GHz mini can come close in performance to the lower end iMacs, but for another $100 you step into the iMac line with TWICE the hard drive space and some other pros. You CAN load up a 1.83GHz Mini to match the 17" iMac specs, but you're at the same price without a display, keyboard or mouse. The iMac comes with all that.
For a nice machine, if you have the money...the 17" 2.0GHz iMac is the best bang for your buck, IMO. But it's twice as much as a 1.66GHz mini, so think about what you need and how long you want to keep the computer around until it's time to upgrade.
Hope that helps.
-Nick