If you're doing light editing and little to no rendering, any modern mini should be fine. I'd consider nothing less than a 2010 (C2D CPU). If you find one with only 8GB RAM you can later upgrade to 16GB.
If time is a consideration and/or you're doing a lot of rendering, then I'd consider a 2012 mini with it's superior GPU, and maybe try to find one with an i7 (quad-core processor). I use this and rendering is much faster than the C2D mini. Using iSTAT menus I can see all cores firing when I render with VLC. Handbrake is also multi-core aware.
Memory for either of those minis is older now and a little pricey.
The 2014 mini doesn't have replaceable memory so you're stuck with whatever you get. I don't think there's a quad-core version available, but if you're not rendering, it's moot.