i don't like the list as much due to it varying wildly depending on the country and style ones plays, making some techs extremely good while others quite useless. Though that's kind of obvious of course.
i can give my experience, usually i play poor and small shitholes. sorry for wall of text
army: doctrine is "only" nice to have, perhaps point defense and maybe deep defense being good. muzzle loading rifles are good for engineers against forts so probably important (they are needed because see next) - heavy armament: this one is for me the biggest differnence, if you're poor artillery is just too expensive to field in any meaningful numbers making the whole tree rather useless until you get a bit bigger but at that point you have more research and can catch up on the tech. army leadership ASAP instead of important since military tactics is super important especially if your army quality sucks.
navy: i honestly don't play naval game that much to know how good are the combat but i never have navy large enough for it to matter. either enemy is shithole too and number of clippers wins or they are big and will have way better navy. for me it's only doctrine to get more ports if i have money to actually upgrade them.
commerce: techs after business regulation are pretty useless to me. business banks i;d say important at least due to the farming bonus which makes huge difference for... well agrarian shitholes. after that its kinda useless/nice to have, the tax efficiency is small for the tech cost. with monetary system it's similar. ad-goc is great, private good to have, then useless or nice to have at best, too many rp