I am the king of ultra budget gaming I work with tons of pro-bono refurbs for sale at a resale shop to raise funds for a food bank. We also get a lot of kids excited about Fortnite, Minecraft, etc, that can't afford a new PC or gaming console, so we donate more than a few light gaming/home PCs to families at the food bank.
Because I deal with such a huge volume of disparate hardware configurations, I start to find stellar values in the mix.
One of those happens to be the AMD FirePro V5900.
It's a 2GB GDDR5 card that shows up in the $20 range, like so :
Radeon V5900 2GB
And here's that very card playing World of Tanks like a boss :
V5900 in gaming action!
This is a great option due to the 2GB of GDDR5. They come EXTREMELY underclocked, so grab MSI Afterburner and crank it up a fair bit and it will get even better, far more than you might expect. Even stock it's more than competent though.
As for what the V5900 is, it's a downclocked workstation variant of the Radeon 69xx series. Even though it's a workstation card, it works fine in gaming, and has drivers up to current date/OS :
Drivers for W7/W8/W10 64-Bit
Specs for V5900 are :
40nm Cayman GPU, DirectX 11.2
2GB GDDR5 on 256-Bit Bus @ 64GB/Sec
614Gflops
75W TDP -
NO PCIe Power Cable Needed!!
They're just incredibly unknown GPUs to most people, so the price is absolute peanuts.
And should you have a bit more budget, there's the absurdly great deal on 4GB FirePro S7000, a 2.4Tflop, DX12, highly overclockable secret beast :
4GB S7000
Now stock, these run just a hair better than a Radeon 7850/7870, only with completely passive cooling, and 4GB (!!) of GDDR5. I've managed to OC with a simple 80mm fan plopped on it, well up there to 1220/1500, which puts it into another league.
Anyways, think outside the box. PS, it would help to know which game she is wanting to play, and the system you're putting it into (What CPU, Ram, OS, Power Supply)