I can give you a partial answer as to what weapons were used in the mid to late 16th century as far as artillery is concerned.

By the end of the 16th century Western European artillery fell into four basic categories. You had the largest piece called a culverin which were 24 to 45 calibers long and could hurl a ball up to 7000 yards. Next you had the cannon which was 15 to 25 calibers long and could hurl a 90 pound ball up to 4000 yards. Next you had the pedreros which were 10 to 15 calibers long that could hurl a 60 pound ball up to 2000 yards. Lastly you had mortars which were 3 to 5 calibers long with a wide bore that hurl explosive shot or a ball of 200 pounds in a large arc up to 2500 yards in distance. For all of these artillery pieces the preferred powder was corned powder.

The Ottomans on the other hand continued to use serpentine powder which was less stable and was not standardized for consistency. The Ottomans primarily used a piece called a zarbzen which could hurl a 30 to 60 pound ball and unfortunately I do not know the distance. These cannon were in two pieces for easy transport, but it made it weaker than a solid cast cannon.

Murphy, Rhoads. 1999. Ottoman Warfare: 1500-1700. New Brunswick, New Jersey.

Young, Peter. 1973. The Machinery of War. London, England.

A bit before my period, but I can probably point you in the right direction.

A "howitzer" generally is smaller than a cannon (Or, as they are called in the 18th century, a gun.) and is generally fired at a higher angle than you would fire a cannon. In contrast to the ammunition used by traditional cannon which generally fired solid "round shot", howitzers were often used to fire various types of explosives such as the carcass shot.

A mortar is another type of artillery that, as far as I am aware, was common for several hundred years. A mortar is basically a great big pot that points upwards and fires the projectile at a very high angle. You could vary the range by moving the mortar around or by adjusting how much powder you used. Like howitzers, they often fired explosives, and were mainly used for sieges, since they could fire high enough to go over fortified walls and drop down behind them. Interestingly, mortars were also adopted by naval forces for use in special situations. Ships called "bombs" mounted mortars for attacking land-based fortifications such as the attack on Fort McHenry during the War of 1812.

Rockets were used similarly to mortars, though, they really only came into widespread use in Europe during the later part of the 18th century. Like mortars, they were also used at Fort McHenry ("The rockets' red glare"). They could be fired up and over fortifications like mortars, and I imagine they were quite terrifying as well.

Even the basic cannon has a number of varieties. They came in all sorts of different sizes, from small field guns that could be transported at a gallop in battle to fire and quickly relocate to gigantic guns like the "Dardanelles Gun"

Cannon also came in two different basic types, at least in the 18th century, which is what I am most familiar with! You had normal long guns, which are the cannon you are most familiar with. Cannon could also be classified as carronades which were used on naval vessels. They were short-barreled, but much, much larger than the long guns used on the vessels. So, they provided a huge amount of short-range firepower, especially when used with anti-personnel rounds like grape or cannister shot, which basically turned the gun into a giant shotgun, often to great effect. HMS Victory, for instance, had a 68 lb carronade, which meant it fired a projectile (or projectiles) weighing 68 lbs. You can imagine the sort of carnage that would cause on the crowded deck of a ship.

Unfortunately, books solely about artillery can be hard to find. One of the few that also happens to be a decent primer on the subject is Artillery Through the Ages: A Short Illustrated History of Cannon, Emphasizing Types Used in America. by Albert Mauncy.