So now that I've played through a Monarch

game. I'd like to share my (lengthy) thoughts on achieving this.
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Civics
The worst thing I could have possibly done is switch to Free Speech. At the time, I thought it was fantastic. An extra 2 gold per town (I had 32 of them at the time) and +100% culture to get my borders in Siberia top pop quick. But no, that doesn't help out a military civ. You should stick to Bureaucracy (once you get it) and then Nationhood once you've run through most of Asia.
The next mistake I made was when to flip to Caste System. Yes, you will need to run Caste System, and will for a large portion of the game. However, India has next to no production. It has plenty of opportunity for growth and cottage span, but it can't build at a decent rate even with Ironworks in Delhi. You have to have Slavery until India is built up with Banks, Markets, Libraries, Grocers, well, pretty much everything Mercantilism and earlier.
Here's the quick rundown on what you should do:
Government: Switch to HR the first turn, then Representation for the rest of the game.
Legal: This one is entirely subjective. At some point (usually when I switch from Slavery to Caste System) the benefits of Nationhood exceed those of Bureaucracy. This is usually the case at the discovery of Rifling when conscripts become much more valuable. Switch at your discretion, but never go back once you switch.
Labor: Slavery until India is whipped into shape, then Caste System the rest of the way.
Economy: Mercantilism until State Property.
Religion: None until Free Religion. Your two obvious choices for state religion, Confucianism and Taoism, don't exist outside of your borders. Even if you go with Hinduism or Buddhism, it's unlikely you'll pick up more than 2 other civs with the same religion. Why does this matter? Well, the only way to keep up with the Euros in techs is to trade with them. If we have a state religion besides their own, the negative relation modifier from having different religions will block any tech trading.
Expansion: Conquest, duh.
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Tech Path
Normally, your only reason not to expand is to prevent your economy from crashing. Well, Rhye changed that by putting in some massive tech penalties in for giga-empires. Near the end of the game, every city was adding 700+ beakers to the cost of discovering a tech. In order to stay competitive in research, you must cottage spam and expand in specific waves. But more on that later.
Whitefire's Recommended Tech Path
Sailing
Alphabet
Hunting
Mathematics
Calendar
Code of Laws
Civil Service
Iron Working
Machinery
Currency
Feudalism
Guilds
Banking
Gunpowder
Philosophy
Paper
Education
Liberalism
Nationhood (Free Tech unless Economics still gives the free GM or we traded for Engineering and can pick up Chemistry)
Representation
Democracy
Engineering
Chemistry
Scientific Theory
Communism
And you know what's odd? There are barely any military techs. I know it makes sense to go down the Rifling route, however, thats the same route the AI goes for. Why research the same techs as the AI when you're unlikely to be attacking them for some time?Many of the techs listed above can be traded for. In my game I got Hunting, Iron Working, Currency, Guilds, Feudalism and Machinery in trade. The last 4 were all from trading Civil Service. Beyond the road to Liberalism, there are two choices you have to make. Do you want Representation or Communism first?
In the end, both give roughly the same effect (200+ gold less in maintenance = 200+ beakers). Whichever path you decide to take, the AI probably won't. They're busy beelining to Assembly line, so you can, in theory, trade for those techs. I would recommend you go after Democracy first unless you have a Great Engineer lying around. The SoL is one of three wonders I count as vital to our empire. Losing it would be a major blow.
The rest of the tech path will depend on what you can wrest from the AIs. Sadly, the AI knows the cost of a tech for you, and will make you pay through the nose for anything. I traded Liberalism, Chemistry and Democracy for Rifling in my last game. It hurt, but I was in desperate need of anti-Cavalry units.
If you're expanding fast enough to win the Domination victory, don't expect a tech after 1800AD. I took the Aztecs down to one city and they would rather die than let me know how to make Railroads. Anyway, with that in mind, the next tech section is assuming you traded to Rifling, at least.
Economics
Corporation
Steam Power
Assembly Line
Fascism
Why the beeline to Fascism? Well, the AI generally avoids this one, and assuming we've stayed on track, we should be able to pick up the GG. Plus, Mount Rushmore is the third wonder which I count as vital. Since we're not running Police State, having this around will keep us from having to throw commerce into the cultural slider. Plus, I sold this tech to every civ and ended up with roughly 5k. That let me run at 100% research for quite some time.
The rest is up to you. However, I recommend grabbing Fission fairly soon. The AI definitely has Industrialism and is pressing towards Robotics. Once it nabs those Mech. Inf., any chance of taking cities without nukes is lost. However, the other techs are not to be forgotten.
I personally would do Industrialism next. That gives us Factories and our UB. A major turning point in my economy was when I had cities building wealth after constructing Factory+UB. I actually caught up in techs with all but 3 civs. Flight also has it uses. Airports were key in sending units I had produced in Russia and Siberia to Mexico and Peru. Without airports, my first war with America would have ended in a complete loss of the territory instead of a stalemate. Composites is also useful, since you can field Modern Armor. Those units actualy have a chance to down a Mech. Inf.
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Another path to consider is beelining to Internet. Normally I would take this path, but with the steep penalties on research, building it with a decent amount of time left may be impossible.