Not many suggestions seem to be forthcoming and the laptops I have are outside of your budget or bought at a time when medium range laptops were cheaper. Your budget is unfortunately below what the linux laptop vendors I know ship. So, to narrow down your parameters:

• Go for AMD --> less to no issues with Linux
  • will most likely be an “APU” (CPU with integrated graphics) which are OK-ish for gaming --> check www.notebookcheck.net for the APU you find and ensure your game or an equivalent can be played with it
• 16GB is nearly too little (depending on what you do) so try to get 32GB
• Use linux-hardware.org/?view=search_computer to check how compatible your choice is with linux
• 500GB SSD is kinda standard, but as a dev downloading whatever dependencies or compiling, aim for higher (1TB should be enough)

Edit: Why does your gaming laptop have to be replaced? Hardware issues? Often those are quite good for programming.

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The problem with my gaming laptop is that there’s some hardware issues that are pretty costly. I’d rather just get a new laptop at that point.