The question of vertical vs horizontal is really dependent on how the chain and rode will fall. The vertical drop off the windlass is important, if it is too short the chain will pile up and force the rode off the windlass. This is less of an issue with a short chain and long nylon rode, but still needs to be considered.
The only advantage to having a dedicated windlass battery is using smaller gauge wire to connect the battery to the charging source. The charging cables on a 31' boat will need to be at least 6 ga and 4ga would be better. There will be some cost and weight savings by using the smaller gauge wire, however that will be offset by the expense and weight of adding a battery. The battery weight will also be exactly where you do not want it, in the bow.
Adding a dedicated windlass battery can be a bit tricky to wire properly. To charge them off the same circuit they will need to be wired in parallel and they will need to have the same charging profile. Just as important the battery should be of the same age and type, i.e., FLA or AGM. Adding to the problem will be the voltage drop over the cables, the battery nearer the charging source will receive a higher voltage than the further battery which will lead to uneven charging. To further complicate the picture, to properly wire the batteries in parallel and to insure even charge and discharge across the 2 batteries it will be necessary to run 2 additional cables to place them in parallel.
My suggestion, forget the dedicated battery, it won't get you much and will be a pain to wire properly. Use properly sized cables from the largest battery in your system and only use the windlass when the motor is running.
