The best deal is probably going to be looking for a used machine with a 3080Ti. There were several of these made with Intel 12th gen CPU's. That is probably the cheapest way to get a 16 GB GPU. They can be found for considerably less than $2k. Anything with a "3080Ti" where the "Ti" part is super important, has a 16 GB GPU, (the "3080" is 8GB). That was the only 16 GB laptop GPU until the newer Nvidia 4k stuff.

That can play any game, and can run some large models for AI stuff if you become interested. On the AI front, you want maximum system memory too if possible. My machine can only address 64 GB of sysmem. Some go up to 96 GB. I wish I could get like 256 GB.

Just because a machine comes with Linux does not mean the problems are solved. You will find many times when people buy machines that have peripheral kernel modules that are orphaned and not part of the kernel. Orphaned kernels are not real Linux and are like phones. Indeed this is the exact mechanism used to steal your phone and prevent you from using it for its true hardware lifetime.

The real solution is https://linux-hardware.org/. Use that to see what works where. You also need to understand modern secure boot with the TPM chip and package keys. These exist outside of the Linux kernel. If delving into this system is too much for you to deal with or of no interest, just stick to using either Ubuntu or Fedora. These both have a special system outside of Linux that will handle the keys for you. Presently, these are the only two distro choices that do this; not derivatives either, it must be vanilla Ubuntu or Fedora. You won't be able to change anything in kernel space when going this route, but if the keys issue is unimportant, that probably won't be an issue.