MMmm…a MTW 2 thread.
As the Mythbusters would say, ‘Well there’s your problem!’. 
You can’t really play the game (IMHO) like Civ…at least not how I play Civ (YMMV). Research for instance, while important, isn’t as key as it is in Civ. In MTW 2 (and Rome and all of the other ones for that matter) its all about coin. The more coin you get from trade and your cities, the more money you have to spend on whats REALLY important…namely troops and ships.
In general I build up my trading infrastructure first (roads, ports, trading complexes, merchants), then my city health infrastructure…the only exception to this is on the frontier where I build walls and fortifications first if I feel those cities are vulnerable (basically my plan is too keep besiegers at bay until I can bring up a stack and trounce them). I then pick several cities/castles in strategic locations and selectively build up my military capabilities…i.e. in one city I build out the militia line. In another I build out cavalry. In another gunpowder type troops, cannon and such. Etc. In the end I usually end up with several cities that have different units types, and so I can build an army by simultaneously building out all the unit types I need from different cities, then tossing a general at them.
As others have said, look who you are fighting. If its rebels then don’t bother with prisoners…you won’t get any. Also, if you are pressing a nation hard they will get to the point where they won’t pay anymore for prisoners (unless they are in the royal family), so don’t expect to make much money from this if you are putting a nation to the wall. I generally get the majority of my money from sacking and plundering captured cities and castles myself.
In general I keep my cities manned with crappy militia units…and my castles too (even though the units aren’t compatible and you can’t repair militia units in castles).
For core cities/castles its usually enough to have a spear man or two and a few militia archer/crossbow units to keep the population happy (assuming you have bought happyness buildings). In the yellow zone (not quite on the frontier but close enough that they could be raided) I usually like to have 3 spear men and 2-3 ranged units backed by a single cavalry unit. In general thats enough to hold any town or castle against anything short of a full court press (the more fortified towns and castles are ridiculously hard to take by direct assault…sometimes a boy scout troop can hold them against even the most determined assault). In the red zone (i.e. right on the bleeding edge) I like to have about a half stack composed of one or two decent melee units (men at arms, dismounted armored knights, billmen, pikemen, etc), a few throw away spear men (to soak up ladder assaults or assaults through gates or other choke points), and tons of ranged units (good archers/crossbowmen, gunpowder units, especially those armored hand gunners and riflemen) and a few cavalry units. I almost never lose a city unless its really under defended…and generally I only bother relieving half the sieges. I’ve found the computer has a really difficult time assaulting the tough cities…and honestly I have a pretty hard time TAKING one without crippling losses, so I prefer long sieges where the city/castle eventually surrenders on its own.
As others have said, the game will definitely grow on you. I switch back and forth these days between playing my TR patched copy of RTW, and MTW 2 (no TR patch yet, curse the luck). The game is simply put a hell of a lot of fun to play, and the tactical battles can be quite stunning. Also, at least in MTW2, the computer can sometimes do some interesting and quite unexpected things on the tactical battle field…which is always fun.
-XT