I was a total novice to Paradox games as well, when I attempted to play EU III (downloaded the game from Gamers Gate). As many already mentioned, you set your own goals, but the accomplishments are usually loosely reflected on your prestige score.
For me, playing a marginal country like Korea meant that essentially I played as if I was not trying to contend for world conquest. Instead, I went for expanding trade in the region and colonizing. But If you were to invade some country, what I found the most important was having a solid economy and comparable technological footing in land and naval technology. It also helps to forge a military alliance with another country in the region. Failing that, you could set the goal over a longer period of time; by gobbling up smaller outlying countries, you could strengthen the nation in that fashion before going up against a larger foe.
In the beginning of the game, most of far east nations do not have forts, which means you can just occupy whatever territory you invade during war without going into siege mode. So my recommendation is to build all calvary army in the beginning, since they do have almost an unfair edge over infantry due to some bug in the game, but because they are also more mobile. If you have a militarily talented ruler, by all means make a general out of him and use him in ensuing battles; it will literally mean the difference between total victory or disastrous loss. Try to diffuse your forces and make incursions into as many territories as you can, while trying to avoid their big main army. To match the size of a bigger opponent, simply take a loan and build as many mercenary units as you can. Also grab war taxes by all means.
On the diplomatic front, I think it may be useful to use spies to induce revolts and help destabilize the country as much as possible. Also It is also good to pick a national idea that gives extra manpower as well. Inflation as Fez mentioned is very very dangerous, so watch out when trying to earn as much income as possible per month.
After I finished one protracted game, I found EU III addictive and rewarding. For the second game I played England, and the experience was even more rewarding and different, playing as a major colonial power. If you like strategy I think you won't be disappointed, what with the different mods and support from Paradox in the future for a more balanced game.
Actually I am holding small parts of Africa, the spanish mainland, half of denmark and the rest of Scandinavia and my Soviet brothers together with thier brave but dumb mongolian cavalary are riding through Poland. Though I'm dead anyway since I can't hold any of my fronts for long.
