Yay, something that i know a bit about!

My area of expertise is the hundred years war (1337-1453) between England and France, so i will draw all my examples from that conflict. Now, to answer your questions in a random order:

The main purpose of raids during medieval warfare was threefold: 1: Disrupting the economy 2: Pointing out your enemy's inability to protect his lands 3: sustaining your own army without paying for it.

Therefor, the most common (and most effective) raid were large-scale, regional campaigns, where a sizeable army would burn and pillage villages and smaller towns, while castles and fortified towns where left alone. This had the effect of forcing the peasants of the raided areas to flee en masse to the larger towns, which, along with the disruption of supplies caused by burning or stealing crops and other resources from the hinterlands, would cause a famine in the affected towns.

A good example of a raid conducted like this would be the Grande Chevauchée of 1355, Where Edward, the Black Prince of Wales, led an army of 5.000 men from Bordeaux into the counties of Armagnac, Foix and Languedoc, while bypassing the city of Toulouse, where the count of Armagnac had concentrated his army. The English army was able to return to Bordeaux with an extraordinarily large amount of loot, while the count of Armagnac became generally despised in France for not resisting the English army, but in reality, he didn't have a choice, because every time his forces would go near the English, they would place themselves on the top of a hill, or on the other side of a river, where they would have the upper hand if the French decided to attack. This had happened earlier, in 1346 at the battle of Crecy, where Edward III used a raiding campaign to force the French king to attack him while he had an advantageous position atop a hill, and soundly defeated the larger french army. And again in 1356, where the Black Prince led a similar raid from Bordeaux (again), and was caught by a large french army near Portiers, which he also soundly defeated, with the added Bonus of capturing the French King.

As you can see from the participation of both the English King and the Crown Prince in these raids, there was no social stigma attached to the concept of raiding, and both common footsoldiers and mounted knights and men-at-arms would participate.

The raid would usually consist of a large main force, with several smaller warbands (30-200 men in each) mainly consisting of mounted troops, would detach from the main force and plunder nearby villages. The army couldn't afford to split too many soldiers from the main force, as it would put them at risk of a counterattack.

As to the target og the raids, by stealing from civilians, taking cattel and burning crops, they crippled their enemies long-term capabilities to conducting military operations, because of a lack of food and taxes from the villages meant a lack of supplies and wages for the soldiers.

As in all other medieval warfare, and maybe even to a greater degree, the soldiers used whatever tools they had handy. Burning villages and towns added the cost of rebuilding to the enemys losses, so it was a must. Horses meant that the raiding forces could get away before the enemy could mount a counterattack. As for the weapons used, i don't think there was any explicit preference.

Sources: The Wars of Edward III, by Clifford J. Rogers

Western Warfare in the Age of the Crusades, by John France.

Trial by Battle, by Jonathan Sumption.

I hope you could use my wall of words, and i'm sorry if my english is sub-par, but it is not my main language.