Buying new: Basically all of the integrated memory units like macs and amd's new AI chips, after that any modern (last 5 years) gpu while focusing only on vram (currently nvidia is more properly supported in SOME tools)

Buying second hand: not likely to find any of the integrated memory stuff, so any GPU from the last decade that is still officially supported and focusing on vram.

8gb is enough to run basic small models, 20+ for pretty capable 20-30b models, 50+ for the 70b ones and 100-200+ for full sized models.

These are rough estimates, do your own research as well.

For the most part with LLMs for a single user you really only care about VRAM and storage speed(ssd) Any GPU will perform faster than you can read for anything that fully fits on it's VRAM, so the GPU only matters if you intend on running large models at extreme speeds (for automation tasks, etc) And the storage is a bottleneck at model load, so depending on your needs it might not be that big of an issue for you, but for example with a 30gb model you can expect to wait 2-10 minutes for it to load into the vram from an HDD, about 1 minute with a sata SSD, and about 4-30 seconds with an NVMe.