A cottage by itself produces 1 coin no matter what, and goes up by one for each size (hamlet, village, town). If the space produces commerce, they're added together, so a cottage on a river produces 2 coins. If you build a cottage on a luxury resource, it will produce 1 coin + whatever the unimproved resource gives, but won't give you the resource or the extra coins you'd get for improving it. (It will also often look like a fully developed town, but this is just a graphics oddity.) For a financial civ, whenever the tile produces 2+ commerce you get your bonus commerce, so a cottage on a river lets you get the bonus immediately, while one on an ordinary space would need to grow to hamlet size first. All of the changes related to the base space will be a fixed number of extra commerce, you'll get an extra coin or two which won't affect other bonuses you can get.
When you're looking at civics to boost cottage output, remember that pretty much all of the bonuses only affect fully developed towns, not fresh cottages. Emancipation makes everything grow faster (so has no effect on towns), but the +2 commerce from free speech and +1 hammer from Universal Suffrage only work on towns. If you've got a lot of cities with less-developed cottages when you develop democracy (this happens a lot with captured cities), you probably don't want to bother with US and FS to start off with, just emancipation to grow them to the point where US/FS give more bonuses than the alternatives. In my current game, for example, I'm playing the Turks on an Earth map. I only have a few towns around my science city and a ton of fresh cottages around 2 captured cities along the Nile. Since my capital has HE and WP, I'm running Beurocracy instead of free speech since the bonus unit production is far more valuable to me than the handfull of commerce I'd get from FS.
