Indeed, the complicated nature of the Victoria 2 economy is legendary. For example, vanilla tends to suffer from a scheduled late-game economic crash that occurs because money is disappearing from the system and isn't replaced fast enough, combined with factories overproducing goods and going bankrupt. Pop Demand Mod and its offshoots fix this by tweaking the economy so that the crash would generally only occur after the end game, but it is technically impossible to entirely prevent the crash. (But those mods also do a lot of other good things, so you should get into them early during your career.) A lot of things are opaque and hard to figure out after plenty of playtime.
Some of the tips I can think of quickly that might help:
You need to use the "Encourage ..." national focuses, a lot. Sometimes you need to "Encourage capitalists" to get your first few capitalists in each state so that there is someone to invest - if you don't, then you might actually not have any capitalists at all, so nobody who can invest. Encouraging bureaucrats (to 1% to begin with, then more later) and clergymen (to 2% at least) helps with research and education (which translates into research). To get more soldiers, you can increase military spending to get more soldiers all over the board, but you can also use "encourage soldiers" to boost your soldier ratio in a state up to around 4.8%. "Encourage craftsmen" is often necessary to build your first few factories, otherwise you might have nobody working in them, and is probably what you should have your NFs on early during your industrialization if there's nothing more urgent. Later, "encourage clerks" will help you train skilled workers to improve your industries.
About industrialization, a small handful of countries (Britain, France and the like) already have some industry early on. A lot more don't, however, and just like in history, need to have a firm hand guiding their industrialization. Generally, you want to industrialize by getting a state capitalist government and just building factories of your own to start with, then encouraging craftsmen who will work in them and a few capitalists later on. If you can't become a state capitalist, you will just have to encourage capitalists, lower rich taxes and just hope for the best. Right at the start, though, less developed countries often have trouble industrializing since artisans are bound to just run them out of business, so it's often worth waiting until you've picked up a few industrial techs in a decade or two. Later on, you can switch to interventionism and finally laissez faire once your industry has developed. (Of course, sometimes it's not as simple as that, but as long as you aren't in a planned economy, your capitalists will still eventually start to run the economy by themselves. Planned economies don't allow the capitalists to do anything, so you'll have to micromanage everything. Not a good option for a beginner.) What to build depends on what version/mod you play, so just experiment a little. Cement, liquor, shoes, glass and steel tend to be some of the goods worth starting your industry with in my experience. Fertilizer and lumber, on the other hand, tend to fail. Early on, you should feel free to subsidize industries that are failing just a little, at least until you find something successful to replace them, but later on you shouldn't subsidize all that much.
There are also tariffs, which are a bit misleading AFAIK - they don't really work in real life since your pops will buy local goods first if they can anyway. Or at least that's how I know it, this may have changed through versions. Instead, tariffs are pretty much just another form of income that you can use to get more money in exchange for risking strangling a nascent industry. Around 10% tariffs usually doesn't hurt that much, and you can jack it up even more early on when you haven't industrialized that much and are in state capitalist mode, but generally you want to get rid of the tariffs later, I think...? You can use negative tariffs as import subsidies, which is good later on if your factories don't have enough raw goods to supply them being produced at home or in your sphere. Speaking of which, you can sphere nations to force them to trade on your market first, which is great for getting access to more resources for your factories, and a place to sell your goods to, but if you sphere a country more industrially advanced than you when your industry is still weak, you might actually just weaken your own industry as a result. (This was a problem Russia suffered from with regards to its own autonomous Grand Duchy of Finland, for example - an internal tariff allowed a fledgling Finnish industry to develop that ended up outcompeting and strangling some of Russia's own attempts at industries for a while.) You can also raise taxes to get money. Early on, you can safely raise all taxes pretty high if you need money, though I'd keep middle/rich class taxes low if it isn't essential to raise them. Later on, try to reduce taxes on the poor as well so they can promote to higher classes.
Regarding staying relevant, you need three things to increase your rankings: prestige, industry and a bigger army. If you care about your ranking (which you shouldn't care too much early on, unless you are a Great Power that's about to slip down into Secondary Power status, or a Secondary Power on the verge of becoming a Great Power), you should begin with the prestige techs - these give you prestige, of course, but they also give so-called "shared prestige", which depends on how many people already got the tech. For example, the first nation to research Realism might get 5 prestige from a Realism-related invention, the second will get 2.5, the third 1.6, and so on. So getting these shared prestige techs immediately is important if you want to make big leaps in the ranking. Generally, whether you are a Secondary or Civilized power makes little difference early on - the biggest difference is that only Secondaries and up can colonize (which is irrelevant before 1870 in vanilla for most nations due to the lack of enough life rating techs before then, though some, like Portugal, might have provinces with better life rating that they can colonize around 1850).
