This page has a list of all the factories on the server and how to set them up.
This should be the first factory you make, unless you have the materials ready for an ore smelter. It takes 8 stacks of charcoal (4 more for fuel), and produces 2 stacks of charcoal per stack of logs, and produces charcoal from coal at a 1:1 ratio, making this factory twice as efficient as a vanilla furnace. Once this is set up, your nation and/or town will have a strong backbone on which to build its industry.
Another handy factory is the Basic Smelter. It takes 8 stacks of stone to create, and its most notable use at this stage of the game is making stone for reinforcing. From a single stack of cobble stone it produces a stack and a half of smooth stone, making it vital if you want to build a large city.
The Ore Smelter is as useful as it sounds. It is also quite expensive, taking a stack of diamonds, 4 stacks of iron, and 8 stacks of coal to create. Using an ore smelter, you can process ores more efficiently (for example, smelting 16 diamond ore gives you 48 diamonds). This factory is vital to any settlement and once it is created, you'll be able to get your economy on its feet. You can also crack the fossils you get from mining here, but do be warned, most of the time it's just a bunch of useless player heads.
When building a settlement, what is the one block that you will always use without fail? That's right, wood. The Carpentry Factory helps you make wooden accessories. It's one of the least expensive factories in the game as well, with the low, low cost of 32 chests.
Iron Tool Forge
Until your nation/town gets the manpower to start large scale mining operations, then you'll most likely be saving diamonds and won't be able to make any diamond tools. In that case, the iron tool forge will be your best friend. All it costs is a stack of iron too, making it extremely affordable. It makes 15 pickaxes for 15 ingots, making it a whopping 3 times as efficient as vanilla crafting.
Rails are the primary mode of transportation on the server, so building a rail tunnel is a good way to get your town to trade with others. All the rail factory needs in terms of materials are 8 gold, 32 redstone, and 64 iron. The recipe for rails is 8 stacks per 2 stacks of iron and 16 sticks, making it essential for all railbuilders.
This is one of the more useful factories. The compactor condenses a stack of one item into a single item, making it very useful for moving tons of stuff around. The recipe is a stack of pistons, half a stack of iron blocks, 16 redstone blocks, and a half stack of chests.
(unknown to me what this does, please put here). The iron forge is made with 2 stacks of iron and a bucket of lava.