1. Chieftain. I'm increasing my difficulty first with increasingly larger worlds before I go to a higher difficulty.
Larger map-sizes are actually easier to play on, not harder, since the number of Civs doesn't scale with the land-tiles available (i.e. even on Huge maps with 16 Civs, each Civ has more land available than do each of the 4 Civs on a Tiny map). It takes a lot longer to finish a Huge game though...
Also, playing Chieftain doesn't teach you how to win at higher levels: quite the opposite, since the Chieftain-AI is so badly crippled (everything costs them twice as much as it costs you). I'd suggest you skip straight up to Regent, where the 'only' production-advantage the human player enjoys is his/her brain...
2. Not aiming for a particular one right now ... that's part of the dilemma.
If you want to win a Civ-game, then ideally you should start each game with a specific VC in mind, and pick a suitable Civ for that VC, even if every other map-setting is Random. That helps you to focus on what you need to do to reach that VC.
Of course, if you'd rather role-play nurturing your Civ to greatness, just sort of bumbling through, and responding to whatever the game throws at you because that's more fun for you, that's your choice -- but playing like that is less likely to result in a 'win'
per se, never mind a quick/efficient win.
I have eliminated Diplomatic as a possibility, though, and maybe Domination (in case I want a Conquest).
Do you mean that you disabled the Diplo-win option at the start, that you've been such a jerk to the other AI-Civs that they all hate you forever (and will never vote for you), or that you just don't want to go for it?
3. 21 towns, including ones I've captured.
That's... not very many, for a game that's gone nearly all the way to the end of the Industrial Age. Can I take it that these towns have been placed at something approaching Optimal City Placement (Cxx(x)xC, distance 5-6 between towns)...? If so, you might be interested to know that most of the better players here argue for placing towns initially at CxxC ('tight placement', distance 3-4), which generally gives better results for the early game -- which is the more important bit! Basically, since you won't be able to use all 21 BFC-tiles of an OCP'd town until Sanitation comes in, more than halfway through the game, planting towns in that pattern to start with means most of your territory gives no return on investment.
As a compromise between these two, you might want to try placing towns at C1xxC2x(x)C3, and then abandoning C2 later, after C1 and C3 have Hospitals: Imagine placing 3 x 3 'permanent' cities on a 'perfect' OCP grid, covering a total area of ~15x15 tiles with their BFCs, but having four 2x2 blocks formed by the unused 'corners' of those BFCs. By placing one additional 'throwaway' town somewhere in each of the unused 2x2 corner-blocks, all 13 towns would then be able to get up to Pop11-12 in the early game, and still have enough tiles available to keep (nearly) all their citizens fully employed. After Sanitation, the permanent towns would get Hospitals, while the corner-block towns get shrunk/disbanded by building Settlers/Workers, freeing up tiles for the 9 potential Metropolises (which could also rehome those Workers/Settlers, for faster than natural growth).
4. With so many units, a few towns have a token amount depending on their remoteness. Most towns have a rather generous amount (considering 538 Infantry, 116 Tanks, and still some Cavalry, plus some Artillery and naval units).
You have >25 Infs per town?!? That's at least 10 times more than you 'need', especially for Chieftain level, running a government that can't use mil-pol. Were you just building them because you couldn't think of anything else...? Even Wealth might have been better: you'd have far fewer useless units (you can't really use Infs for attacking, and passive-defence is not the way to win wars), and a lot more gold-income that way...
I have more units than I've ever had before ... cranking them out at an incredible rate. But I've built everything I can build already, except in a few captured towns I'm still building up. (Railroads nearly everywhere by this point.)
This is partly why your economy's suffering. Building everything everywhere is -- sorry -- a typically n00b mistake, which I used to make myself. Unless a building contributes to your intended win-condition, it's just costing you gold which you could be using for something else.
Aztecs in Vanilla are REL+MIL, giving them cheap Temples, Cathedrals, Raxes and Harbours, i.e. they're best at doing War or Culture (or the one followed by the other!), and beating techs out of their victims until they're big enough to research stuff themselves (if they haven't already killed everyone by that point). So why build Libs before they're needed? Or Banks?
Again, that's why I don't know the best way to go, except maybe for Conquest despite other civs' MPPs.
MPPS aren't a problem, especially not at Chieftain. Pick your target, make MPPs with all their 'friends', then declare war but DON'T commit any aggressive actions against them on their territory (killing their units on your territory will not activate hostile MPPs). Allow the target to commit the first act of aggression (maybe leave a Worker somewhere vulnerable): once they do, all their Protectors will DoW them, which will break their MPPs, allowing you to go on the attack without fear of reprisal.
Even at higher levels (say, up to Emp), you can usually get away with doing this, provided that your borders are secure (and with >500 Infs, they should be!)
I don't build Destroyers ... I just wait until I can get Battleships, of which I have six. I would gladly get rid of my Cavalry, but don't know what they would go into, because there is nothing left for me to build in most towns except military units.
I prefer Destroyers to Battleships: they're quicker to build, they move faster, and for shore patrol, they're really all that's needed: it's very easy to redline enemy ships -- even Battleships -- using Artilllery, then sink them with a Destroyer (a full-health A=12 v/eDestroyer almost always wins vs. a redlined D=12 Battleship). Battleships are useful for guarding invasion-fleets/ Carriers, by taking the initial punches from enemy shipping, but that's about all.
I'd probably use the Cavs+Arty for homeland defence against incoming fast units (the dangerous ones!), once the war(s) start: bombard to redline, then use Cavs for the kill. Best case, your Cav wins, gets promoted or gives an MGL; worst case, it dies, saving you the unit-support until you've built a Tank to replace it. You could give your reg-Infs some target-practice the same way.
