Hi, I'm a gunsmith in Sulphur Springs, Texas. Here's how that went down;

hunting for this lesson has to be rightfully confined to a european context, and thus excludes asian and african norms. hunting was primarily the right of the nobility; on horseback the landed gentry would hunt wild boars and deer with spear, but in practise these hunts were cavalry exercises, with bugle calls and the like. Hunting for food was rare and largely fowned upon socially, as hunters/furriers were seen as lazy outsiders, and not hardworking farmers and tradesmen.

From the 1650s guns would have been used, but would have primarily been pistols, as the long barreled musket would have been hard to use when mounted. The musket, normally of about 10 bore, had a cousin which would have been used, called the caliver, with a shorter and lighter barrel of about 16 bore, which might have been used.

In all the hunting weapons of the time were spears and crossbows, with proper portable guns not being common in gentry hunts until the wide acceptance of the snaplock, which begat the proper French lock of 1703 - today we call it the Flintlock, but the true term is indeed the French lock. If a regular man went hunting [or poaching] he did so with a bow and arrow, probably self made, and very few would risk the legal foil of using a gun, which could be heard by grounds keepers and game wardens from far off. [guns were expense anyways and out of reach for people who were still really serfs.] It was not until the rise of the liberating grand arme of the French Republic that guns, albiet military surplus, were within the reach of large amounts of people [french army = best army, french legal code = best legal code]

If we extend our view into the American colonies we see a vastly different picture. There were no great boar hunts with spears on horseback, as the colonists had guns from day one. There were also crossbows, but guns were much desired. After a narrowly won battle during King Phillip's war, the colonists scrambled to aquire snaplocks to replace their older matchlocks, which had to be lit and could not be kept lit long term - as oppossed to a snaplock which was a grab and go weapon.

And as for accuracy - the inaccurate musket is a myth plain and simple. Rifles were for the rich, as on the whole, were the rare exemption, not the rule. Rifles took longer to load, they took special bullets and tools, and it was not until the minie ball was developed [french army= best army] that rifle could be used to any real extent en masse. For hunting, they were mostly unwanted, save for a few competition shooters and hunters. There were so costly that even Davy Crockett was known to have only 2 in his life, and one was a gift by the state of tennessee.

The common man had a smoothbore fowling peice [basically a light musket of about 20 bore, whereas the 1600s musket was about 10 bore], and could load ball for big game like bear, buck and ball for the same or deer, buckshot for deer, and shot for fowl. The musket did it all, and can still do it just fine. This was the case regardless of the form that gun might take, be it the matchlock, the snaplock, the trade musket with it's french/cap lock, all the way to right now - with the shotgun.

On more modern note; look into the old sears catalogs, you'll see that shotguns were pushed hard, and being smoothbores, where quite similar in use and loading to muskets. Rifles did not outpace smoothies in the catalogs until the mid 1930s.