Techs we must have to build nukes:
Printing Press
Replaceable Parts
Gunpowder
Rifling
Astronomy
Chemistry
Scientific Method
Steel
Physics
Artillery
Electricity
Rocketry
Fission
I'll post an image of the tech tree with techs highlighted.
Other tech paths that might make teching or warring faster:
Education-Liberalism-Communism (requires SciMeth also)
Nationalism-Constitution
Biology (requires Chem-SciMeth)
Education-Economics-Corporation-Steam Power-Assembly Line (requires Chem and RP also)
We also need to know what Great People will want to bulb (necessary techs bolded):
Great Engineer
Great Scientist
Great Merchant
Great Engineers are good early. The first one can bulb the majority of Gunpowder. The next one would bulb about half of Chemistry if we don't have Printing Press or Education or Nationalism yet, or otherwise parts of Replaceable Parts (or Economics or Constitution). Chemistry adds 1 hammer to workshops while Replaceable Parts adds 1 hammer to watermills. GEs can also bulb Steel or Steam Power. With a free specialist available at the beginning with Mercantilism and with an engineer the only type we can hire immediately, a GE is very likely to be our first great person, and a second GE is also probable.
Great Merchants will bulb Economics, Constitution, and Corporation if we have Education and/or Nationalism.
Great Scientists have the most value (giving the most beakers and bulbing the most needed techs). The first one would want to bulb Education. But if we trade for Education, next in line are Printing Press, Chemistry (if we don't have Astro yet), SciMeth, Astronomy, Physics, Biology, Electricity, and Fission.