Is it faster to build a worker, followed by a settler, or the other way around?

In Civilization IV, both workers and settlers prevent your city's food store from increasing for as long as they are being built. Surplus food is funneled into the production of both units, speeding their creation.

A common dilemma I have at the start of the game is deciding which one to build first. I'd like to get a settler out as quickly as possible, to start another city. But without any farms, surplus food is low, so it will take longer to complete.

Alternatively, I could build a worker first, set it farming, then build my settler. Workers are significantly cheaper to produce than settlers. Perhaps the extra lead time to produce the worker would be offset by the accelerated production of the settler. But producing both the worker and the farm(s) takes time.

In general, given that I ideally want a settler as quickly as possible, is it a better strategy to build the settler first, or the worker? Are there any other factors to consider?

I think the biggest thing to consider is the surrounding terrain. If you have some kind of food source (rice field, cattle, etc), then I think that building a worker would be the best move. This allows you to have a solid food supply, and it will improve the build time of a subsequent settler.

If you don't have a favorable location, or if you're on the coast (where you can work the water tiles for food), then I think a settler would be a better choice.

You really have to weigh up the expansion of your empire vs the surrounding terrain. Sometimes it's conducive to quick expansion, sometimes you'll have to consolidate first.

If the only goal is to have a settler as early as possible, then build the settler first. Settler costs 100 hammers, and a city with no improved tiles produces 4 hammers per turn(including food converted to hammers), so that's 25 turns. A worker is 60 hammers, so that takes 15 turns. In a best case scenario, the worker can immediately start chopping forests for 15 hammers every 4 turns. After 14 turns, the worker has produced 45 hammers, and the city has produced 56 hammers and the settler is completed. That's turn 29 of the game, 4 turns later than if you had started with the settler.

But I don't think that getting a settler as quickly as possible is the most important goal. Usually the best start is to build a worker while researching the techs so he can immediately begin improving a very strong tile like pigs, cattle, or wheat, corn next to fresh water. That will get you a settler on about turn 32, plus a worker and 1 to 3 improved tiles.

If you want a settler as fast as possible, that will come from building the settler first... but the fastest way to get two settlers out is to build a worker first.

Also, you should always consider the threat of wild animals and/or barbarians (assuming you play with them on) which could kill an undefended settler. You also need some time to scout around for the best spot for your additional cities.

Thus, it is generally advisable to get a worker first, followed by either another worker and then a warrior, or just a warrior before you really consider getting a settler up.

It will almost always be faster to build a worker first, then a settler. The worker can be improving your tiles while you finish the settler, and so your production will go faster. Also, the worker can build roads so that the settler will reach its destination sooner.