I second skipping over the motherboard for a budget-but-upgradable build. Video card is the most important thing, so as long as the motherboard supports it, it's good enough, and the vast majority will.

That said, second hand graphics card still isn't a bad idea, since when you're finished with the build some years down the line, the video card will be the oldest component.

Instead, get an NVMe M.2 hard drive, and a PCIe expansion for it since that budget motherboard probably won't have native support. Expansion cards costs hardly anything relatively, and native support can be added to the list. A great hard drive makes ok RAM better than OK and cuts level loading times significantly. Honestly, adding a great hard drive to even some tiny budget dell desktop with built in graphics makes an ok budget gaming computer.

If there's money left over get a good sound card or whatever peripherals you'd prefer, maybe Wi-Fi/Bluetooth (budget mobo probably skips them) and RAM if the budget mobo is still a recent one. Despite the TV likely being good enough, too. I wouldn't focus on the motherboard until you're picking out the high-end CPU, which is expensive but also just a lower priority than the other stuff, so a good monitor is on that peripherals list, too.

That dell comment is from experience, I made one into a surprisingly decent Minecraft/Roblox machine for a relative. Only thing that stopped it was the HDD it used. A solid-state drive is sufficient, m.2 is just future-proofing.