I'll throw my oar in with an example of a game I'm playing at the moment. Note that I'm a Prince player but I'm playing a Noble game.
Up until recently my starting tactic has been to research all resource techs for my capital, then BW. I rarely MM'd the capital, and my build order was always;
Worker > Barracks > Archer > Archer > Settler > Worker > Archer > Settler > Worker.
This worked fine when I was playing Warlord level games, but in Noble and Prince I found myself getting beat to the best city spots so, I changed my tactics, and this is about the 3rd game I've tried it on, albeit circumstances where favourable.
More often than note, you capital is capable of producing a lot of food, whether that be through resources or farms. My capital had a few floodplains, cows and corn. Since floodplains give 3F, I decided Pottery was a priority, and Agriculture then Animal Husbandry. I started with Mining and BW was next.
I had discovered I was on an island with Hannibal as my only companion, nd in my experience he can spread like the plague, so I needed to get Settlers out fast.
Whilst researching the above my build order was;
Worker > Barracks > Warrior > Settler > Warrior > Settler
You can see this is going to get me Settlers quicker than my previous tactic. Also, Barracks is there for growth...whilst building barracks I'm working high food tiles at pop 2, then pop 3 will work a mine. The Barracks may or may not be built by the time pop 4 comes around, but if it does, I alternate max production for warriors and max food for settlers completely ignoring my research rate (although in this case I was working a cottaged floodplain, so my research rate was pretty good).
The primary aim for the two Settlers I'm building depend on the surroundings, it turns out that I can block Hannibal with one well placed city. So that's where the first Settler goes.
The second Settler would have gone to get bronze but the only supply was under Carthage. This made Iron a priority, but the second settler found a good gold city spot.
Note that in my initial new cities, I build Barracks > Archer/Warrior > Settler > Worker again MM the cities to alternate production and food.
This allows me to fill in the rest of the island fairly quickly before Hannibal can get Galleys around my borders. By this time I've researched IW and my food monster capital start whipping Praets (I was Augustus). Swords would have done the job almost as well.
Note that at this point I'm still not particularly concerned about research rate or health and happiness in my cities, but the Workers have been busy building the infrastructure for when I stop whipping and let cities grow.
150BC and I have taken all four of Hannibal's cities with Praets.
So, 150BC and I have 8 cities. I now go into peaceful expansion with a general beeline to Optics after getting currency for markets (forums in this case).
I've build no wonders apart from Chichen Itza (purely for GP points as I wanted the Confucian shrine). Yup, founded Confucianism as well...mostly wanted Courthouses.
So that's my general game plan for the BCs. Obviously it deviates when the need be, but as long as I can get settlers out fast and beat the AI to the best sites than you should be OK for an early war to take AI cities before some peaceful economic revival.
Don't be scared of the whip, happiness soon recovers especially as you start hooking up happy resources...let them grow into unhappiness and whip infrastructure buildings like courthouse or even theatres if you need a culture boost.
In summary, I don't particularly concentrate on my research rate, happiness or health until the AD's, but Workers are building the infrastructure in readiness.
Blimey, that was longer than I expected it to be.