Intro

Regardless of what faction you play, the first part of a TW campaign is always the same. Protect your borders keeping the smallest army possible and build an economy.
Protecting your borders doesn't necessarily require a full stack army in each border. Use all the possible tricks, these include allies and protectorates as buffers (don't be afraid to give away a poor border province if it greatly decreases the extent of your borders). Set your armies in ambush positions, use spies to see attacks before they reach your borders, etc. Also, keep an eye open for opportunistic attacks that will allow taking a neighbor province, but only if this doesn't increase your borders or put your defense under further stress. For instance, liberate them and create a buffer. It's important to do so with the smallest army possible so that you can invest more money instead of spending it on upkeep.
Building an economy is simple. You get money from tax income and trade income. The former is increased by infrastructure, admin buildings, commercial towns, etc. That's what you should invest on. Keep the building of military buildings to the absolute minimum (required for technology advances). Trade relies on getting access to trade nodes and therefore requires a navy which is clearly easier with same nations than with others.


France

France has 3 concerns. Eastern front with Austria+Russia, Northern Front with Prussia if/when it joins the Coalition and Western Front with the Brits.
Swap Hannover with Prussia for their closest province and techs. Prussia will keep it cool while you don't go on the offensive.
Use your allies on the East to keep Austria at bay. Keep an army in Northern Italy and another in the Strasbourg ready to support your allies if (and only if required).
Keep an Army around Paris for the inevitable Brit landing.

You want to build an economy and if Taxes are trivial (just apply the already proposed building approach), Trade is tricky with the French because of the Brit naval superiority. Given so, your goal should be to eliminate that superiority. Run with your atlantic fleet to Rennes avoiding Nelson at all costs. Upgrade your dry dock there. Use this fleet to keep Nelson in check and possibly attack the weaker fleets to get new ships. Once the dry dock is complete, build as many big ships as you need to take out Nelson. Once this is done, blockade every Brit port and go after its Trade Nodes. Start pumping out Trade ships. The Med on the other hand is easier and you can get some trade nodes from the start since Nelson will be busy on the Atlantic.

Once you get a very good income, get an extra invading army then go to Sicily, Naples, Papal States (at which point Italy will declare war on you). Have southern army take Milan immediately. From there Austria.
Once you go on the offensive, Prussia will join the coalition, so be prepared with armies on the northern front. Take Hannover back and be prepared for a lot of full stacks coming from Berlin. I took an army by boat and blitzed/looted the coastal provinces. Then I kept two full stacks in Hannover. Prussia kept sending armies and when they didn't I would advance and take the University, forcing them to attack again. Eventually they run out of full stacks since they can't replenish as fast as you (having lost so much wealth from the coastal provinces). Forces that attacked Austria can go North and help complete the job.

Finally Russia. To succeed where Napoleon failed. At this point it shouldn't be very hard since you can field several full stacks to get the job done. Still, I took it to the point where I barely fought any battle with Russia once I went on the offensive. Using two stacks from Konnisberg and two other from Romania, I went through the lines and took all russian provinces adjacent to Moscow with barely any resistance. I was able to do so in part because I liberated Courland and gave all these provinces to it. Being it a recent nation, Russia wasn't immediately at war with it. By the time it did declare war, winter was upon us, I had headed to French provinces (Warsaw and Konnisberg) to spent winter there. The russian armies on the offensive tasted a bit of their own medicine with the cold. Once spring came, I marched my 4 stacks to Moscow, defeated the two full stacks there and took Moscow. Game Over.

Note: You dont need to take GB or Ottoman, but both can be annoying and force you to allocate forces to keep them in check. Ottoman I used protectorates as buffers once it had only Greece and Rumelia. GB I ended up taking. Started with Ireland and Scotland. Liberated the latter and convinced them to declare war on GB. This forced them to spread their forces making my naval invasion easy.
Note 2: When I took Konnisberg from Prussia, I also took the western province and gave it to one of my allies with whom Prussia wasn't at war. This created a partial buffer which was enough to keep the bulk of Prussian forces (the ones at Berlin) from storming me. It also served as a bait for Russian forces who came stack after stack to be defeated. Russian Armies are far weaker than prussian ones and far inferior in Artillery, one of the strenghs of the French.

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C.