Reddit mentions of Acer Aspire AT3-710-UR52 Desktop, Intel i5-6400 processor Quad-core 2.70 GHz, 8 GB, DDR3 SDRAM 2 TB HDD Win10 home

Yeah, very bad design, confirmed with Amazon reviews. How can those idiot make this in 2016?

To use the GPU you have, unplug those wires - from left to right they should be: front audio, front USB2, front USB3. You can at least test to see if the board even boot with a video card, since it don't even seems to be designed for one.

Some single slot RX 460 are being planned:

http://techreport.com/news/31028/xfx-rx-460-core-slims-down-to-a-single-slot

http://www.tweaktown.com/news/55108/tease-single-slot-radeon-rx-460-slim-icooler-oc-4gb/index.html

Most single slots card in the market are very weak cards like GT 710, which the iGPU inside the CPU is probably better.

https://www.amazon.com/Acer-AT3-710-UR52-Desktop-processor-Quad-core/dp/B01A0ZRXCW/
Be careful about the power supply, it might not be able to support a GPU.

Honestly if you aren't willing to build yourself your best bet would be to get a basic core i5 desktop and install a graphics card yourself.
Something like this Acer for $450 with about $100 or so graphics card like a GTX 750 Ti or an RX 460 wold be good.

You don't need much for your requirements.

Second the option of a Thinkpad though, the E560 or E450 would be a great option.

Or, if you prefer a tower, you can check out this.

do what i did for low budget...buy a prebuilt pc with decent specs then slap a 750TI in it and a 500 watt power supply instant 300+ fpson 1024x768 stretched and 200+ on 1080p with high settings heres a good start and it's WAY better than mine is...just get like a gtx 1050 TI and you're set... https://www.amazon.com/Acer-AT3-710-UR52-Desktop-processor-Quad-core/dp/B01A0ZRXCW/ref=sr_1_5?s=pc&ie=UTF8&qid=1484265525&sr=1-5&keywords=acer+aspire+desktop