min_p author here. min_p is strictly better than top_p and top_k. The big labs don't know shit about sampling, and give absolutely nuts recommendations like this.

set min_p to like 0.3 and ignore top_p and top_k and you'll be fine.

There's better samplers now like top N sigma, top-h, P-less decoding, etc, but they're often not available in your LLM inference engine (i.e. vLLM)