Do you do any video editing?
I play games like Battlefield 3 on my iMac and i know that the Video editing and 3D artwork uses a lot more resources than playing the latest games.
Also remember that if you get a Mac Mini then you will be without an optical drive unless you purchase an external drive. I seldom use mine but i know others that use them quite frequently.
Since you mention price is an important factor, don't overlook Apple Refurbished Macs. They come with the same warranty as new Macs & are refurbished to "like new" conditions.
The last two iMacs we bought were refurbs & they have been just as problem free as any brand new ones we have bought.
I was looking at this the other day and decided an iMac (21 inch) is the way to go. Here's why: yes the Mac mini is cheaper, but by the time you add in a decent monitor you are nearing the price of an iMac. Plus, the iMacs are a lot faster. You'll get more life out of an iMac and it has more expandibility as far as installing memory. When it seems slow add more memory for $100 or less depending on how much and pricing at the time. The Mac Mini will fill up and seem slower before the iMac. Plus, the iMac has the optical drive and thunderbolt.
Top Mac Mini: $799
Apple mouse + keyboard: $118 ( not included with the mini )
Apple MacBook Air SuperDrive $79.00 ( No DVD/CD drive included with the mini)
24" LCD around $170
Mini display port to DVI adapter to connect LCD $34.00
Basic webcam around $40.00
Total for Mac Mini: $1240
Total for iMac 21": $1199 Including; keyboard, mouse, monitor, superdrive,webcam.
The iMac as a quad core i5 versus a dual core i5 in the Mini.
So in the end, the price is almost the same, but with the Mini you can replace the LCD for under $200 if it is dead in a few years.
Changing the LCD in a iMac will cost at least $500.00
You can also reuse the LCD bought with a Mac Mini with a other computer later on.
It's up to you!
THis is a no brainer fomr Mac Mini...but one from the refurb site...get the latest i7. Get 16gb memory for crucial, put your own SSD in it and buy a 27" ips (no Apple) screen for about $350 from an alternate vendor. I have this setup on my desktop at work for under $1200 and the ability to replace things in the future with little hassle. Plus you get better ports on the Mini for legacy items such as FW800 that Apple should be embarrased they ommited on the new iMacs. Nobody needs a superdrive...it's 2013!