His family isn’t wealthy by all means. [not correct] His family is by no means wealthy. [correct] His family isn’t wealthy by any means. [correct] The phrase "by all means" doesn't fit here. It usually means something like "certainly" or "definitely," especially in a suggestion or a command: "By all means, don't tell my parents!" / "By all means, bring your friends if they want to come!" (I believe it's roughly equivalent to 千萬, as in "千萬要來".)

His family isn’t wealthy by any means. im choose

The 2nd one is fine but uncommon.