There's a lot of doom and gloom about the 2007 iMac, but I can only speak from experience. I've had that exact model since Day 1 (came with Tiger) except I've added 6GB of RAM and a 128GB SSD along with a 1TB Firewire 800 drive, and also now runs Yosemite. Anyway, I absolutely love it and it is still my main computer. I do all the normal everyday stuff along with a lot of Garageband X. If anything caused me to get a new computer it would be running into CPU issues with Garageband, but I'm not a professional and haven't gotten there yet, and even if I did I know how to lock tracks among other workarounds And yes, the monitor is still pretty great IMO.
Point is my computer is worth far more to me that the $200-250 I would get for it. Even if Yosemite is the last supported OS, there will still at least be security updates 2 1/2 years from now, which isn't bad at all for the price. Would it be a good buy to me? Absolutely. I think of it this way: if you only spend $200 or so on a computer, and it can perform for a couple years, especially with the build quality/ease of use of Macs, then it was well worth your money.
Now with the proposed model, you'd definitely have to add RAM, and an SSD would be nice, but I don't think that one is required unless you want quicker boot up times and quicker times for opening apps.
But thattttt being said, if you have a keyboard/mouse/monitor, a current gen refurb Mini proposed by the OP would be a fine choice as well.