I finally won my first game on Monarch, after 3 losses. Thanks bonscott, I read this thread a couple of weeks ago & used a lot of your advice

Especially the parts about the techs the AI doesn't usually research, more military and non-stop trading.
I had been playing on Regent level and couldn't remember the last time I lost so I decided to kick it up a notch. My first 3 tries on Monarch were losses. First I played as the Ottomans and tried a premature Archer storm against the Aztecs but got permanently messed up by Jaguar warriors on the counterattack so I aborted. Then I tried as Korea and stayed in the game until the industrial age but was too far behind in tech and got overrun by huge stacks of Infantry. Next I tried as the Babs and was doing pretty well, second in land area for a long time through to the early Industrial Age, but then got overrun by the Iroquois, and again when I was behind on tech.
My last game I selected default rules, large map, 11 opponents, everything random. I got Spain, which I was initially not too thrilled with but when it became clear that the map was an archipelago, 80% water I started liking them a lot. I also liked the Conquistador more than I thought I would. It's great for exploring. Seafaring is obviously good for archipelagos and Religious is always a good trait. My initial island fit 7 nice cities, plus a tiny island next to it which I put an eighth city on. This wasn't huge, but enough to have a good base. I sent a bunch of galleys exploring and found Carthage with some islands nearby that he had expanded to. Fortunately I had Iron and so I sent galleys with swordsmen and medieval infantry (couldn't afford the upgrades since I was spending a lot on research) to deal with three islands, gaining a total of 7 more cities. I then waged another war to gain a foothold on Carthage's main island of six cities, waited 20 turns to let the peace treaty expire, then wiped out the rest of the island, now with mostly knights, medieval infantry and a sweet knight army. Then I basically just hung tight, having enough land.
It was still early but most of my enemies had decent armies so I didn't fancy the prospect of a big inter-continental invasion. I got a lead in tech with the ToE prebuild, and the AI were all fighting so their tech rate dropped. I kept a pretty big military but stayed peaceful. The Incans were leading me on score (is it me or does the AI play that Civ really well most of the time?) but I was gaining on them. The Russians, Iroquois and Americans were all at near tech-parity with me, usually 1-3 techs behind for the rest of the game after I got ToE. I would sell them techs at outrageous gpt, I think at the end I was getting 700 gpt in trades. Basically if at least one other civ had a particular tech, I'd sell it to everyone. Or, if they had a tech I needed I'd trade with that civ and then sell to the rest. I went for space race. Got an SGL with about 5 techs left that I needed for space race, so I chose the Age of Discovery and the game was over in pretty quick order. The Americans had 3 parts built at the end. My first Monarch win
One amazing bit of good luck the Mongols had in that game, they had one not-too-big island with about 10 normally-spaced cities and all 8 resources! Why don't I get that sort of luck?! They didn't expand anywhere though and were WAY behind in tech so it didn't matter.
Just started another Monarch game last night. Got Portugal (that has to be one of the worst civs), large map. Got off to a good start but I'm still behind in score by a lot. Not many luxuries, but a good production base and short borders. I've already waged a couple of very successful wars. I'm behind by a couple of techs but I think I'll be able to extort those after my next war

I turned off the space race criteria, since I always end up using that.