So, what am I doing wrong?
Is it just a matter of building more towns? and if so, what is the optimum target? At what number can I consider that I have enough to get me to Superconductors? Or is it something else that I'm missing?
One of the first things is that Russia definitely is the best civ for a Chief/Huge/Spaceship. Barbarian setting is Sedentary. Now as Russia you'll build several scouts in order to reap all those goody huts and quickly meet other civs. Pretty much all of your ancient age research will come from goody huts, although you might want to research some techs the normal way in order to have a few shots at SGLs.
With just a little bit of luck, you'll enter the Middle Ages in about 2000BC.
Wrt to expansion ... Getting a free settler is very convenient. Make sure that you are eligible to actually get one, i.e. you are at or below the global average number of cities, you have no settler active and no settler in production. While you have a settler active you can still get a free town, though. So, optimally you get both, a free settler
and a free town before you have built any settlers.
Getting an SGL early is also very important. You kind of have to try to hedge your bets and adjust your real research to your goody hut research and vice versa. I would probably select my 'opponents' so that there are no religious civs on the map, and then research Ceremonial Burial, Mysticism, Philosophy and take the Republic for free. Those are four shots at getting an SGL in the Ancient Age. Needless to say, that if you get an SGL you'll use it on the Pyramids.
That said, you need to keep on expanding. Once you have so many towns that they are corrupt you'll have to make Science Farms as well as you can. Smaller ones, larger ones, tiny ones with just one geek. The answer to the question "How many cities do I need?" is not a number; it is rather "Get as many cities as you can and as you need", being able to research Robotics (that is the most expensive tech, right?) in four turns should be your objective. Science Farms don't really need any improvements. Although, in some cases a Lib is not wrong or there is enough food to warrant an Aqueduct.
Keeping your people happy ... well, look out for luxuries. Preferably within easy reach, otherwise scrutinize the coast lines of your continent for luxuries (and crucial resources) that are on the coast or just one tile in. Then send out a galley, caravel, or what have you laden with a settler and maybe a worker to settle these spots. Just settle right on a luxury or resource if it is on the coast. The town needs a harbour, but otherwise you can just turn the one laborer into a geek, put the city on wealth and forget about it.
If you don't have enough luxuries to keep your people happy, don't be shy to hire geeks. Three beakers isn't so bad.
Otherwise there is of course the lux slider. On Chieftain with 10% lux you can get a lot of people happy.
The timing of your golden age is also kind of important. Early middle ages is ideal, although that is not always manageable. In the end, try to get a good bang out of it and not to waste it.
You know how the age change tech trick works, right?
(I hope that^^^ makes some sense.)
ETA: This thread could be very helpful:
http://forums.civfanatics.com/showthread.php?t=392651&page=4
That's the Oct/Nov 2010 gauntlet: Chieftain, Large, Spaceship