You can find most popular models converted for you on huggingface.co if you add exl2 to your search and start with the 4 bit quantized version. Don't bother going above 6 bits even if you have spare vram, practically it doesn't offer much benefit.
For reference I max out around 60 tok/s at 4bit, 50 tok/s at 5bit, 40 at 6bit for some random 7b parameter model on a rtx 2070.
For reference, I'm getting 10 t/s with a Q5_K_M Mistral GGUF model.
Pretty much anything with ~6-8GB of memory that's not super old.
It will run on my 6GB laptop RTX 2060 extremely quickly. It will run on my IGP or Phone with MLC-LLM. It will run fast on a laptop with a small GPU, with the rest offloaded to CPU.
Small, CPU only servers are kinda the only questionable thing. It runs, just not very fast, especially with long prompts (which are particularly hard for CPUs). There's also not a lot of support for AI ASICs.