OK... I've played a few games, won a little, but still not sure I'm getting off to an "optimum" start. I'm sure that there are probably 100 opinions as to what optimum is... The answer to everything is "it depends", but tell me - am I heading in the right direction here.
I start with one settler and one warrior (or scout). I prefer the warrior - better survival rate.
Settle as close as possible to the place where it starts. Next to a river is good. Next to an ocean is also good.
Build a warrior. Build another. When city population reaches 3, build a worker, then a settler. Then wait for more growth and build another worker.
Meanwhile, send your warrior out looking around. Objective is to (a) find huts and get gifts. (b) Find location for next city. (Coastal would be good, if first location was inland.) (c) locate opponents.
Meanwhile, you have to research. This is where there seems to be a lot of disussion. I want to be able to build cottages a.s.a.p. Then I go for gunpowder.
When you get your worker, set him to building farms - leading to city growth and then cottages - for commerce.
Once your second city is established, let it grow and then build worker and settler.
So, is this an OK starting approach? Or what could I do better? KEEP IT SIMPLE!!
Of course: 'it depends'

There is no formula to do things right in civ IV.
I prefer going for terrain improvements as early as possible (and I know some other players who I consider knowledgeable about this game who'd agree with me). An improved terrain tile will produce a lot more resources especially if you consider that 2 food from each tile is used to feed the population working the tile.
An unimproved grassland cow tile adds 3 food, from which two is used to feed the population working the tile, so a net gain of 1 food. A grassland cow tile with a pasture adds 4 food and 2 hammers, so a net gain of 2 food, 2 hammers. You can see that an improved grassland cow tile is far more interesting. Improving the land around your cities quickly will increase the speed with which your civilization and your economy grows.
For that reason, I often start by researching a worker technology (based upon the resources that I see around my capital) and I will start building a worker from the start. The worker will be finished just after the worker technology has finished and then I'll start improving the terrain. Sometimes, I will start with a workboat first.
My starting warrior will explore and after the first worker, I will often build some more units to start exploring. Scouts have the advantage that they can't get negative results from goody huts (like barbarians). The chance of negative results is larger on the higher difficulty levels. Warriors are a lot better when barbarian warriors and archers start appearing. I usually go for warriors because I play at high difficulty levels and the warriors and archers appear earlier on these levels. At the lower difficulty levels, a scout might be worth it. It can explore more quickly and you get combat bonusses versus the barbarians at the lower difficulty levels. It might allow you to explore extra goody huts before the AI gets them.
I will keep improving the terrain, chopping forests, researching new worker technologies, further improving the terrain and expanding my number of cities. To support the increasing costs of expanding, I will build some cottages. I try to get new health and happiness resources while expanding so that my cities can grow larger without getting unhealthy or unhappy. I also try to get strategic resources to get better units for defensive and maybe offensive actions. I explore the area with my units, so that I know the good spots to settle my cities. I don't want to sent my settler into territory that hasn't been explored before.
Gunpowder??? That has nothing to do with the starting period of the game.
By the way. If you start by researching an early religion, then you might not have finished any worker technologies before your worker is finished. In that case, you shouldn't build a worker first.