The gypsy on most modern windlasses will handle both rope and chain. For instance, the windlass on my boat has a gypsy that is designed to handle 5/16" G43 high-test chain and 9/16" or 5/8" nylon rope. The chain size is very specific to the windlass gypsy, and putting the wrong size chain on the gypsy can damage it..
The capstan, or drum, which projects above the gypsy on some windlasses, like mine, is used for hauling in an all rope anchor rode. If the windlass is a vertical design, like that in the drawing I posted, the drum can also be used to haul up a dinghy via a block and tackle or halyard led to a snatch block.
Vertical windlasses, however, require a deeper chain locker for the anchor rode to fall properly. They tend to be a bit more secure in holding the rode, since they take a 180˚ wrap on the gypsy, rather than the 90˚ found on a horizontal windlass. They’re a bit more useful, as the capstan can be used for things other than an anchor rode as mentioned above.
A horizontal windlass is often a better choice for a boat with two anchors and two bow rollers, since many horizontal windlasses have the gypsy on one side and the capstan on the other. They require less distance for the rode to fall into the chain locker, since the rode only wraps 90˚ and is dropping off the gypsy or capstan into the chain pipe. Here is a lighthouse horizontal windlass:
Either horizontal or vertical windlasses can be operated remotely if they are properly setup and equipped with a bow roller that pivots and self-launches. To set the anchor, you would free it—undoing any lashings or pins that secure the anchor while underway. Then you would either let the gypsy freefall or let out some rode. This would allow the bow roller to pivot under the weight of the anchor and self-launch the anchor. I prefer to control the rode feeding out rather than let it freefall, since it is far less likely to end up in a pile on top of the anchor and possibly foul the anchor and prevent it from setting. As the anchor is dropping towards the bottom, you would allow the wind to push the boat backwards a bit....until you have enough rode out to set the anchor. Many anchors can be set at 5:1 scope, but you would be wise to let out 7:1 or 8:1 scope if conditions are going to be rougher....