I've increased my total budget to about $650 and put together a parts list. I left out the graphics card because new ones are too expensive, so I'm planning to buy a used one separately. I'm completely new to building PCs, so I'd appreciate advice on anything I should replace, add, or change. I'm considering a used Radeon RX 5600 in great condition for around $140 including shipping. Please focus on improving the PC build rather than suggesting a console.
2 Answers
The build seems reasonable for the budget, but you definitely need a graphics card because that processor does not have integrated graphics. The GPU will be especially important for gaming and will take up a noticeable part of your budget. A used RX 5600 for about $140 could be a decent match if it has been tested and works properly.
At this price point, compare the total cost with complete used gaming PCs. Buying a whole used system may give you a stronger processor and graphics card for the same money, while building with all-new parts can leave less room for the GPU. If you stick with this build, make sure the power supply is from a reputable brand and has enough wattage for the graphics card.

I found a used Radeon RX 5600 in great condition for about $140 including shipping. The seller has a strong approval rating, so I’m considering using that as the graphics card.