Due to potential size considerations, I've made a post out of this, rather than replying to the
_guy_incognito post that spawned this little essay. So when I say "you," I am referring to the specific "you" represented by Mr. Incognito.
Commerce issues in Civ 4
Several of your questions seem to revolve around your money supply, so I'm going to address fundraising in Civ 4. First up, the stuff that costs.
In my experience so far, upkeep for your army isn't a real problem. Upkeep on your cities, however, is. It took me a while to get past my Civ 3 "more cities == better" mindset, but once I did, my finances straightened out admirably. Basically, each city past your second costs additional upkeep, and as you add cities, the amount of increase caused by the next city increases. There are plateaus at 2 cities, 6 cities, and 9 cities; there's a significant spike at 10-11 cities. This can be hard to see, though, because the additional city doesn't just get assessed all the new upkeep, it gets spread around a selected group of cities. So your seventh city will increase upkeep in some number of the previous six. Moreover, upkeep increases the further from the capitol that the new city is, with breakpoints at 7 tiles, 11 tiles, 16 tiles, and 20 tiles. There may be more after that, and diagonal tiles count as 1.5 horizontal tiles.
So step one is to make sure that you're not outgrowing yourself-I had an empire go completely bankrupt with units disbanding themselves every turn for centuries once, when I overextended by taking (rather than razing) barbarian cities.
Step two is to make sure your cities are connected. Connected cities share trade routes, and trade routes increase commerce. Notably, cities on the same river are automatically connected, as are cities sharing a coast. This means you don't need to waste worker time building a road between them for the commerce benefit; it can wait until you need faster transit for units.
Step three is open borders. You get more commerce from trade routes if you share open borders with another civ. Of course, this has other ramifications: if you're trying to cut a rival civ off from a portion of the continent, it's probably not worth it. However, it's worthy of note that upon a declaration of war, units inside the enemy civ's borders are moved out. So you don't have to worry about the other civ pre-positioning units outside your cities.
Step four (which might actually be step three in terms of execution order) is cottages. Build them, and build them early. You need pottery and bronze working to build a cottage, so keep this in mind when you're beginning early research. Now, you don't have to beeline both techs and slap cottages down everywhere; they only grow if they're being worked. So I generally wait for cities to have a few citizens, then toss a cottage down on one of the tiles they're already working. Often, I'll pick a forest/plains tile: the forest chop will hasten whatever the city's building, which is nice in the early game. Bear in mind, though, that you won't be able to build a lumbermill there later (unless the forest regrows, obviously). My order of priority with early worker improvements is (in general): farms, cottages, mines. Particularly if a city has a food resource in its radius (e.g. rice, corn): I'll toss a farm there for the health benefit and the massive food output, and then devote other plains tiles to cottages.
The military
As for upgrading units, I almost never do. It's just too expensive. Every now and again, I'll upgrade someone that's got some XP, since it carries over...but by and large, I'll just build new. Keeping your army up-to-date is tough, but it's also not terrifically necessary. If you get a couple good defensive units dug into your cities, you should be able to hold off most attacks for long enough to get your mighty war machine rolling with new units. Archers, longbowmen, machine gunners are all fantastic city garrison units. Build them in cities with barracks, give them the city garrison upgrade, then fortify them in cities. It only takes a couple each to provide pretty solid defense. Once you've got horseback riding, keeping a few mounted units around for mobile response is often handy. They move 4 tiles on roads, so you can generally have one unit cover a couple cities (in terms of being able to get to the incursion in time).
I will generally disband and replace rather than upgrade units. When I start rolling out archers, for example, I'll move the archer to the city, then disband the warrior. It's more important to build your units in a city with a barracks than in a city that needs them (except when you're currently at war).
If you're maintaining a defensive army, I'd recommend trying to keep two of your best-available defensive units in each city. This isn't easy, so a rolling upgrade plan with border cities getting first dibs is in order. This also assumes you've got a tech lead, or at least are pretty much even with other civs. If you're behind, you need to increase the garrison size. On the other hand, if you've got massive city garrisons, the Hereditary Rule government civic will give you a +1 smiley face for each unit in the city. Once you've got machine gunners, you're pretty much set for defense. A couple of those fortified in an established city will give just about any attacker, up to and including modern armor, a tough time.
An offensive army is trickier. You need combined arms stacks to be really effective, particularly for city attack. Military units in Civ 4 are pretty much a rock-paper-scissors game, so a uniform-unit stack will generally be surprisingly vulnerable to someone. Also, don't underestimate the power of the medic promotion. If you can keep a medic in your stack, do.
If you're taking cities any time later than the very early game, you're going to need catapults (or cannon, or bombers...anything that can bombard). The city defensive bonus plus the cultural defensive bonus is a real kick in the jimmies, and the AI is generally smart enough to put city garrison upgraded units in its cities. You're facing, easily, a 100% strength bonus in a reasonably defended city (+25% city garrison, +25% fortified, +50% cultural bonus), even if the city doesn't have walls, isn't on a hill/in a forest, and you're not attacking across water (don't do this). That turns even your average archer into a 6, which matches a horse archer, a swordsman, and defeats and axeman. A few turns with a couple catapults bombarding every time, though, will do wonders for your chances.
Great leaders
Engineers I tend to save for rushing wonders, unless I'm so far behind in tech that even that won't get me the wonder. And if I'm that far behind, burning the GE on a tech is generally my response. This is particularly effective if I can build the Taj Mahal, since that triggers a golden age. That gets me a wonder and its bonuses plus a golden age for half the cost of a normal golden age.
Prophets I use to build the wonder for a religion I've founded if possible, otherwise I turn them into super specialists. Prophets are pretty damn annoying much of the time, and a waste of a great person. I tend to pick wonders and assign specialists to avoid great prophets if possible as soon as I'm out of the early game.
Artists, it depends. On normal speed and a standard map, GAs give you a +4000 culture bonus for their masterowrks, so it's a question of if you've got enough turns left for their per turn culture boost to add up to more than 4000, if you're trying to culture win (bearing in mind any multipliers, as from spending money on culture). If you're not going for a culture win, though, the +4000 is often preferable. It's particularly potent in border towns with opposing civ cities nearby; it can easily be the trigger for culture flipping their city. It's also a good way to seize control of a resource that's just outside your borders (and/or inside theirs), or to pacify a city you've just taken. So, really, it's situational.
Scientists build academies, all the way. I'll only use a scientist for anything else if every one of my cities already has an academy.
IMHO, you're right, golden ages are overrated. I've occasionally used great people to trigger one when in the middle of a war, but aside from that, I haven't bothered. Eight turns just isn't long enough, in my mind.
Which civs
Depends on my strategy. If I plan on relying heavily on religion, I'll be sure to pick a Civ that starts with Mysticism (or you can kiss the early religions goodbye). Then I'll beeline for Judaism, picking up Hinduism in the process. You can't stop the AI from getting at least one of the early three religions, in my experience.
If I'm shooting for a domination win, there's no beating the Aggressive trait. That free XP is really helpful all the way through the game.
The rest of the traits are pretty much even, in my mind. Creative is really nice in the early game for expanding your borders, freeing you from worrying about obelisks or Stonehenge. It fades into irrelevancy towards the mid/late game.
Philosophical is nice; Great People are good to get; it's a solid wild card if I'm not sure which way I'm going to play.
Expansive is nice for the late early game, early middle game, which is when health really starts to put a pinch on city growth (at least, in my experience). Certainly by the modern era, though, it's useless.
Financial is a fantastic trait, though it only really takes hold once your cottages have started growing into hamlets. But it goes a long way to alleviating all your money woes. I tend to go with a financial civ more often than not.
Organized is the ugly half-brother of Financial. In my mind, it's simply not as good as Financial at preserving your wealth, and doesn't offer adequate offsetting advantages. Sure, it's nice in the late game when you've got more cities, but by that time it's not really necessary. Many disagree with me on this, though, so grain of salt it.
Industrious has the potential to be fantastic, but I find myself not wanting to spend the time on wonders more often than not, so I often skip this one. Really, I should rectify that.
Unique units
The fast worker has one extra movement point per turn, so it can move 3 instead of 2. This is a nice bonus, particularly in the early game, but fades into irrelevance as your road network grows and your number of workers increases.
The rest of the unique units are pretty much interchangeable if you have no idea when you'll be involved in wars. Their primary discrimanting factor is when they become available, so if you've noticed a pattern in when you normally end up being attacked, you can try and pick a civ with a UU that comes in around that time. For example, the Americans' UU is the Navy Seal, a late game unit. If you're the sort of player who avoids wars if at all possible, this is a good choice. If the AI sees you're about to win, it will often just decide to attack. This happens in the late game, and is generally unavoidable, so having your UU in the late game is ideal.
Whew
That got even longer than I feared.