The unique is actually the factory, but power plants are still amazingly good when you're stacking them 5x like we will in the heartland.
The funny thing about district costs is that they scale with whichever is more advanced of tech or civics... and not only is the civics tree smaller, but we also plan to get to the end of it. So, we're kinda hosed if you're trying to keep district costs down. (besides, we can't actually "turn tech off" in the civ 4 sense...)
Here's the full list of techs for factories, which is to say Industrialization (boosts in parens):
Shipbuilding (2 galleys if we really want)
Mathematics (3 different types of districts built)
Education (earn GSci)
Mass Production (Lumber Mill improvement)
Industrialization (3 workshops)
Here's what we need for the Eiffel Tower, which is at Radio:
Military Engineering (build aqueduct, if we really want)
Stirrups (get Feudalism civic)
Gunpowder (build an Armory)
Metal Casting (own, which is to say upgrade, 2 crossbowman)
Ballistics (build 2 fort improvements with military engineers, if we really want)
Steel (build a coal mine, assuming our coal doesn't appear under a district)
Power plants come at Electricity, which requires:
Industrialization (see above for details)
Cartography (build 2 harbors; welp)
Square Rigging (kill a unit with a musketman; I find this terribly hard to do if I don't get in a war)
Steam Power (2 shipyards; requires harbors, so nope)
Electricity (own 3 privateers... actually, they're pretty decent units because of when they show up)
While we're here, Electricity is the only prerequisite of Computers (have a government with 8 policy slots), which doubles all tourism output.
The last building for theater squares comes at Radio, along with beachside resorts.
It requires these notable things (this list is backwards due to many prereqs being covered already):
Steam Power (direct prereq for Electricity)
Flight (build an industrial or later wonder... like the Ruhr Valley or the Eiffel Tower)
Industrialization (see Industrialization above)
Scientific Theory (have The Enlightenment civic)
Astronomy (Build a university building in a campus adjacent to a mountain)
The one other thing we really want in the tech tree is Printing, because it doubles our tourism from great works of writing.
It requires:
Iron Working (1 turn out)
Engineering (build ancient walls plus a sliver, or 4 turns)
Machinery (boosted)
Printing (build 2 universities)
Other techs that could be interesting:
Banking is useless to us except that it adds a gold to our quarries. It leads to Economics, which is completely useless to us. However, that leads to Replaceable parts, which gets us modern farm adjacency bonuses. Radio leads on to Advanced Flight, which reveals aluminium... we only care if we're worrying about aircraft. If we're really hurting for stuff to do, Computers leads to Robotics (Have the Globalization civic), which gives our pastures +1 production.
At our current tech rate, all the stuff I listed above is going to take 3-400 turns. Obviously, population growth is going to improve that for us, and getting most of the boosts will cut that down a lot. Still, even if we don't build a university in a campus next to a mountain, we have our hands full for longer than I think we want this game to take, if we don't build at least a little research power. We probably don't even need the 2 campuses to accelerate the things that require two. (Those, actually, only save us a few turns, now... it's the modern era stuff which starts taking 20-30 turns.)
Meanwhile, for civics, we want Mass media (Cristo Redenetor and Broadway).
For that, we need:
Recorded History (half-done; to boost, 2 campus districts)
Feudalism (6 farms)
Civil Service (10-pop city)
Medieval Faires (4 trade routs; lol no)
Guilds (2 markets; welp)
Humanism (earn a Great Artist) -> this unlocks art and archaeological museums
Diplomatic Service (Have an alliance with another civ... probably not)
Mercantilism (earn a great merchant... hah)
The Enlightenment (earn 3 great people)
Civil Engineering (7 different specialty districts... by locking out 2, we may not be able to do this)
Nationalism (Declare war using a causus belli.)
Urbanization (Grow a city to 15 population)
Mass Media (research Radio)
We also want Exploration along the way for the Merchant Republic:
Military Training (build Encampment)
Mercenaries (have 8 land combat units)
Medieval Faires and Feudalism (in above list)
National Parks require Conservation, which branches off from Mercantilism and Urbanization:
Colonialism (Research Astronomy)
Natural History (build an archaeological museum) -> also grants zoos, the first area happiness building
Conservation (Have a Neighborhood district with Breathtaking Appeal; I haven't, historically, built many neighborhoods, but that's the place to build them!)
Conservation leads to Cultural Heritage, which gives us a card for doubling art tourism.
Honestly, not only is that second list shorter, but the research times seem faster, too. That's what we get from a ton of culture districts, though (and sometime, we need to build buildings in them...).
Actually, to give a concrete piece of advice, I think this should be our beelines, in order:
(Machinery,) Industrialization, Electricity+Radio, Printing, Steel, Computers. We could move steel forward, if we really want to raise tile appeals already, but it's almost kinda in the "it'd be nice" category anyway. Computers may even be better. Printing should be researched whenever it's convenient and we've got some writings. Although, to be fair, the Forbidden City is a pretty good wonder. If we research it early, we might even be able to get it.