Sims 3 on a 2014 Mac Mini

@2009_JW  Your saves would work fine on the digital version of Sims 3, provided you've registered your base game and packs or could do so now.  There's no need to use discs if you can install the game through the EA App.  And you wouldn't have to deal with the 2 GB RAM limit that comes with the 32-bit Mac version.

Having said that, if you're set on an older Mac that can run Mojave, anything with an AMD Radeon Pro graphics card would do.  The Vega would be fine but is overkill; you'd see similar results with a Pro 570 or 580.  I ran the game for a while on my 2017 MBP with a Pro 560 and have tested it on an iMac with a Pro 580; the Pro 4x0 series is basically as fast, with the 5x0 series having been little more than a refresh.  The 380 would also be sufficient.

The graphics card is the important factor here, not the processor.  So a Xeon CPU wouldn't do you any good unless it were paired with a suitable GPU, and a lower-end CPU than a Xeon would also be fine with the right GPU.

If you're set on going this route though, I'd suggest using your discs to install the game on a Windows PC.  The discs themselves would work equally well, and the Windows version of the game is superior to either Mac version.  I can get into why if you like, but the short version is its RAM limit is ~3.7 GB rather than 2 and it's a lot smoother and doesn't have the extra bugs of the 64-bit Mac version.  And a decent gaming desktop for Sims 3 could cost U.S. $800 or so, often less on sale.

You could also Bootcamp any Intel Mac and get the benefits of the Windows version while keeping macOS around for everything else.  My 2017 MBP is Bootcamped, and once I did that, that's how I played Sims 3 for a while, despite having it installed on the Mac side of the partition as well, until I built my gaming desktop.  It would cost you a Windows license, but that's it, and for me at least, it was well worth the price.