It depends on how I was trying to win - by conquest, domination, science (diplo/spaceship), or culture. To be honest, I don't play with either of those civs very often.
America is industrious and expansionist, so you can leverage those traits to build up a very productive empire quickly. I would make sure that I am NOT producing a settler in my capital and pop a few goody huts right away to get a second settler. Or you can get techs (including Alphabet) from huts. So I would found Washington, build 2 additional scouts and pop as many huts as possible. Near Washington, I would be creating roads on the good tiles and be maxxing science. I wouldn't be going for the Great Library at Monarch level because if I was expanding right with good commerce, I'm going to be light years ahead of the AI on science. And when they do get a new tech before I do, I will simply trade for it with them.
I've never played England. I like the early game advantages of America, though.
Also, after a while you learn the techs that the AI prefer and the ones they tend to avoid. They always avoid Literature. So you can research it and get whatever Ancient Age techs they've researched in return for Literature - it kind of works like the Great Library without building it that way. In the Medieval Age, they start to go for Music Theory and Printing Press while you can stay on the hard science path to Invention / Gunpowder / Chemistry and then trade that away for whatever they've done. In the Industrial Age, they will always go for Communism / Fascism / Espionage while you can have Electricity and Scientific Method to yourself. Build the Theory of Evolution and pick Atomic Theory and Electronics and you will have a huge lead - you can trade those for just about any Industrial Age tech you want.
But the most important thing is to figure out what kind of victory you want. If you want conquest or domination, science is kind of irrelevant except for the good military techs like Iron Working (Swordsman- 3 attack), Mathematics (catapult), Feudalism (Pikemen 3 defense and Medieval Infantry 4 attack), Chivalry (Knights - 4 attack, 2 move), Engineering (Trebuchets), Gunpowder (Musketmen), Metallurgy (cannon) and Military Tradition (Cavalry). At very high levels like Sid and Deity and Demigod, some players just build up their civs until they get Military Tradition, convert tons of Horsemen or Knights to Cavalry, and just absolutely rip through AI's with huge stacks of cannon (or artillery) and Cavalry. Some of the most famous games involve shredding multiple Sid AI's in a matter of 50-60 turns.
If you want to win by culture, you have to decide that before the game. 20k culture in one city means focusing all of your efforts on building Wonders in one city. It's also extremely important to be ahead on science to generate Scientific Great Leaders to rush Wonders in the 20k city. By contrast, 100k culture is all about building an empire as large as you can as fast as you can and then building as many cultural buildings (Libraries, Temples, Universities, Cathedrals, Colosseums) in your cities. It's the only type of victory where Feudalism can be best because you can population rush buildings. Science is almost irrelevant, and there is no tech after Education that really helps you with culture until you get to Computers. You've probably won the 100k game by then.
If you want to win by science (Diplo - building the UN first and then holding a rigged election, or Spaceship - researching and building parts first), then it's focus on roads, building a huge empire (every city produces at least one uncorrupted beaker), and building out science capacity (libraries, universities, Colossus, Copernicus' Observatory, Newton's University).
If you go to the Hall of Fame forum, my thread on my Hall of Fame attempts basically tracks what I've learned about victory conditions and how to play for them over the course of re-learning and re-playing Civ 3 over the past 10 months. To be fair, some of those early posts show me very raw in my game and some of the games I put in the HOF are pretty poor compared to more recent games. If anything, I've learned it's about being ruthlessly dedicated to your victory condition and early game expansion. Food = population = production & commerce = power.
