Well, a newb to EU3. I've played plenty of other grand strategy. (Particularly Crusader Kings and Victoria 2.)
Bucked my normal habit of trying to make my first game as hard as possible (and fought the urge to pick the Cherokee, which seems like a fairly hard way to start the game, especially since I imagine I'll be constantly fighting off Europeans before long.) I went with England in the Grand Campaign. It seems like I need to get Trade to 7 and Government to 4 before I can go colonize places. Both of those are at 4 now. I've been starting wars with France while I wait to get Trade to 7. However, I have the following question: Colonization seems to be the main point of EU3. The sooner I can colonize (and especially if I'm the first major power to be able to do so) the more of an advantage it seems like I'll have. So, here's my question: Is it worth it to just stop fighting, disband the majority (but not all. I'm not an idiot.) of my army and just put every cent I can into getting Trade to 7? Seems like it might be worth it to put myself in debt and take out loans if needed. I also got an advisor who gives me a plus to Trade and that seems to have helped quite a bit. Any opinions? I don't think I need anything else to start colonizing after Trade gets to 7.
Also, what exactly is the point of sending merchants out to trade centers? They don't seem to be doing very much. I stopped sending them out as a test, and nothing seemed to change in the game. I had initially assumed it would bring in more money, but that doesn't seem to be the case. Maybe I'm doing something wrong.
If it makes a difference (and it might), I'm playing with all the expansions. Thanks!
(n.b. - wrote more than expected. jump to bottom for nice summary)
First: You very astutely observed that colonization is one of the main points to EU3. It is definitely important to get Trade Tech 7 asap for the Quest for the New World national idea. However, especially in singleplayer, the AI is not terribly efficient at colonization, so while you should not waste time getting the requisite tech for that idea, you can afford to wait until Government Tech 9 to get it as your second idea. It's a better use of the first idea, especially if you're also fighting France to entertain yourself in the interim, to pick something you can use until colonization time and simply spend your second idea on QftNW. So get Govt Tech 4 and take your first national idea - make it economic if you're ignoring the continent, Military Drill if you aren't - then start researching in Trade Tech until you start getting penalties for early research (you'll see them as "This technology is X years ahead of its time" on the tooltip for the research area in question on the Budget window), then stop to pick up Production and Land Tech until the penalty goes away, then research Trade and Government Tech to 7 and 9, respectively, switching from one category to another when you hit the early research penalty again. (Milestones for Production and Land Tech are 4 and 5, respectively; PT 4 gives you Constables, which, when built everywhere, give a significant boost to your annual income, while LT 5 unlocks two new infantry units which are significantly better than their initial counterparts.)
In short: Colonization is important, but you'll get there quickly enough in singleplayer just by focusing your research on Trade and Government Tech. It's definitely not worth taking out loans over.
Second with regard to military downsizing, the optimal path for reducing military costs is to keep higher numbers of regiments at lower maintenance. You can adjust your maintenance on the Military window. The AI, when calculating which countries to attack, will look at (and weigh heavily) how much of your force limits you have in active troops, but *not* the maintenance of those troops in question. So if you have a force limit of 20 regiments, the AI will think you stronger if you have 20 regiments at 50% maintenance instead of 10 regiments at 100%, even though the price and effectiveness to you is the same. If you don't reasonably expect rebels, you can keep maintenance at 0% for maximum income, but I've personally found 50% optimal because you can put down rebels easily, you take less time to get to 100% maintenance if you get attacked and have to move the slider to full maintenance to fight the war, and you're still saving significantly from full maintenance, even if not as much as you could at 0%.
Third, with regard to merchants: When I said colonization was one of the main points, I did mean one, as in there are others of equal importance. I regard the trade system, being representative of the evolution in economic policymaking and the uniting of local trade markets across an ever-expanding global network during the colonial era, to be every bit as integral as colonization in getting the full EU3 experience. Unfortunately, because the actual economic management of the game is a bit deceptive at first, it's hard to notice at first glance. Explaining trade makes more sense in light of the general economic system so I'll cover that.
EU3's economic system operates on a monthly basis. Every month, you get a certain amount of income from up to five difference sources. First one is taxes; all provinces produce tax revenue of varying amounts. If you click a province, you'll see its tax value. That value is the annual value, so you get 1/12 of that per month. The second one is production income; all provinces produce a certain trade good, and your working class citizens, in producing that good, generate revenue for the crown. Just like taxes, you'll see the annual value of the production in the province by clicking the province, so divide by 12 to get the monthly revenue. If the province produces gold, it's treated a little differently and filed under Gold Income, which is a third area of income and also found on the budget tab. If the province is overseas, then it does not have a production value, but rather a tariff value. Tariffs are the fourth source of income; they act like production income, but run on different modifiers. And, finally, there's trade. The production value of a province is derived from its trade value, which can also be seen on the province window. That trade value gets sent to the Center of Trade to which the province is tied. The sum of all trade values of all provinces tied to the COT constitutes the COT's value. When you place a merchant in the Center of Trade, your merchant takes home 5% of the COT's value (multiplied by your trade efficiency) as trade income.
The reason you didn't notice a bump in your treasury is because your monthly income, by default, is invested in research. What you would have noticed is a bump in your research investment. You can more clearly illustrate this by playing a short (i.e. 20 years and stop) game as Holland. Boot it up, cancel your alliance with Hainaut on day one, and you don't have to worry about military matters. Then look at your budget window to start; you'll notice that your income is pathetically small, because you're just a 2-province minor. (You're actually rather rich for being a 2PM, but objectively you're still poor.) Now, take those 20 years and trade nonstop. (Make any slider moves toward free trade until full, then put them in plutocracy.) By the end of those 20 years (if not sooner, from adjusting your budget), you'll be able to check your budget window and find that your income is MUCH higher, because you've been trading.
Of course, while a higher research base is nice, this doesn't matter much if you're going broke because you don't actually make money. So what can you do to actually get spendable cash instead of automatically-invested research? There are two things. The first is your annual census tax. When you hit the start of a new year, all your provinces pay their total tax value (modified further by other factors) directly to the treasury as a census tax. This is how you can afford to run your inevitable (at least for a while) monthly deficits. The second is minting. You've probably noticed a seventh slider after the first six (five techs + Stability) for the treasury. When you increase this slider, you cut down your monthly expenditures by holding on to some of your money instead of researching with it. This is called minting. Minting is good to a degree - especially come colonization time, you basically need to mint to keep colonial expenses from utterly destroying your economy, and later on you'll want to mint at least a little bit to maintain a strong military to match the AI (which is notorious for minting almost all of its income to maintain the highest possible troop levels). However, minting will cost you some tech advancement compared to not minting, and minting past a certain point will cause inflation. I have found the best minting strategy for the first half-ish of the game to be to mint about 10% of your income (which means getting inflation reduction of -.1/yr; hire a 5* Master of Mint and this is covered); you'll find yourself with an initial surplus, which gets spent on heavy early colonizing, allowing you to reap better dividends from your colonies, and then later surpluses which can be spent on expensive manufactories when the cash is available.
Basically, you have to mint to get actual treasury benefits from trade (or anything else), and you need to have a sizable treasury to afford colonization. So hire a 5* Master of Mint, move your sliders toward Free Trade and start trading everywhere once you have about a 70% chance to place merchants in COTs.
ETA: Wow, mega tl;dr. Summary:
1. Colonization is a big deal but not worth taking loans and killing all your units to achieve ASAP. Start by keeping high numbers of regiments at low maintenance and focusing your research on Trade and Government tech; aim to take Quest for the New World with your second national idea, not your first, as the AI is incompetent and you won't miss out on anything important (if anything at all) by waiting. (It's definitely more valuable to use that first national idea on more pressing needs instead of putting it off a while to get QftNW a decade earlier.)
2. You were getting benefits from trade, possibly (assuming your merchants stuck) - but it was going to your research investment (default location), not your treasury. You need to mint to take home some of that money. Hire a 5* Master of Mint asap (you can create one with 100% cultural tradition, or possibly find one already available for hire), move the treasury slider as far to the right as you can without accruing inflation, and you're good.
3. To make your trade awesome, move all the way to Free Trade with your government policy sliders asap. By the later 1400s you should easily have 5 (later 6) merchants in every COT you can find and reach, which will basically make you insanely rich for the rest of the game.