First post, so apologies for unoriginal tips (am only on page 14 of these tips). Also, these are findings from warlord/regent difficulty & may differ for other settings.
Inca - A great civ for any maps with goody huts. Not only because they're expansionist, but also due to their 'Chasqui Scouts'. Once you have these moving up spines of mountains you'll uncover far more huts than your rivals.
To ensure you get what you want from these, simply research the quickest tech that you DON'T want (e.g. warrior code). This will ensure that the next 'tech hut' will give you the next quickest tech (ceremonial burial). You can then set your research rate to 0 up until Monarchy or the end of the ancient era.
Typical build queue - scout x 2 (or warrior if other race), granary (switching to temple before it's built), worker, settler, (then worker, settler if city is large enough), Pyramids (or granary), worker, settler, etc.
Despite my favourite Civs being aggricultural I'll very rarely build granaries. As the Pyramids & Sun Tzu's are never obsolete I'll almost always go for these (& get them even in multiplayer). If a city's to withstand the growth from building wonders it should make it's first building a temple. The absence of a granary is rarely felt in your capital (especially if you're aggricultural). Start building your biggest (non-wonder) improvement, clear nearby forests, switch back to wonder & boom, a nice headstart to Pyramids. To further ensure it's completion before others I like to set govenor to prioritise production just in case.
All early cities that would've been building granaries can instead build barracks or wonders of their own until the Pyramid's completion.
War: Vs the AI - I usually find myself way ahead in tech and subsequently suffer the 'demands' of tech from them. Naturally I tell them where to go and let them waste resources/turns trekking all the way to my borders before making peace again. If peace isn't possible then veteran spearmen & javelin throwers are enough to see them off and maybe even provide a free source of workers on my doorstep.
Vs human players - Currently playing a mammoth 4-player (LAN) pangea with most AI dead or not far off. It's a 'C-shaped' custom-built pangea with myself (Americans, tho prefer Mayan nowadays) in bottom left, Arabs north of me, Russia east and Persia top right.
Persia have stopped expansion but have cornered the tech/wonders market and have been embroiled in a recent war over an island with Russia. Arabia have expanded to my borders as a by-product of destroying 2 AI. Their forces are currently rebuilding whilst continuing city expansion east toward Persia. Russia remain a staunch ally sharing my eastern border, but unable to reach the other civs via land.
Having recently researched sanitation and railroads through diplomacy (the only Civ to have both now) I've halted all research and worker/settler 'pruning' of cities. I have ~4 'Rifleman/Cannonx2/Knightx2' armies (1 for nearly each Arab city on my border) which are all within a newly built railroad's distance away.
'Shock and Awe' - If all goes to plan, the unsuspecting Arab nation should collapse within a few turns. With 4 border cities and 3 coastal cities (I have ~dozen privateers) being attacked at once. Then, if the loss of these cities doesn't spark civil disorder, I'll continue to 'buy out' other cities with my ever-increasing (0 science + Adam Smith's wonder) stockpile of cash.
At this point I'm expecting Arabia & Persia to ally. Whilst unworked jungle/mountains may keep them from my front for a few turns, there's no way I can defend such a broad front. And so, I'll be entering into a 'city-for-city' deal with Russia giving them an already railroaded connection to the others via land and leaving me to defend only half my front. These cities also have the luxury of fortresses (built by crusaders) on a collar of mountains to their north, so should stem an anticipated strike from the Persians until Arabia collapses.
Having seen 3/4 of the AI crushed, I've been secretly supplying the remaining AI (located on an island just off Arabia's coast) with techs & will trade them the remainder in exchange for them declaring war on the Arabs during my 'shock & awe' turn.
This is my first Civ3 game of this scale, so may fall foul of bad habits picked up from Civ4 (where I favour using great people as 'culture bombs' to absorb neighbouring cities etc). I'll let you know how things go and if I find any WMD's to justify my unprovoked attack.
Doh...just notices it said 'short' single player tips. So feel free to move this wall of text.