That's a pretty broad range of dates and a pretty wide net, so I will attempt to answer part of the question and see if you have any follow-ups.

First off, a merchant ship (defined as any ship carrying cargo) between 1700 and 1899 could be anything from a very small one-masted ship engaged in the coasting trade (sailing between local ports) to a very large East Indiaman carrying cargo halfway across the world; by the end of the 19th century, clipper ships were crossing the Atlantic in less than 15 days. So there's a wide range of ships that might meet that criterion.

If you're talking specifically about the period of the Napoleonic wars, which spanned the 18th and 19th centuries, we're on a bit firmer ground. Many merchant ships would have no guns at all, or only a few small guns to fight off casual pirates or privateer ships. The largest merchant ships constructed during the period were East Indiamen, used for the trade between Europe and (you guessed it) India. That name technically can refer to any ship chartered by the British East India company, or can refer to any of the ships various European nations used to trade with India, or a specific type of ship. I'm going to focus on the ship type and let you fill in with any questions.

The merchant ships that most resembled warships during the period were the East Indiamen, which were often painted to resemble warships and often carried relatively large armaments (for a merchant ship). The Arniston, for example, which was wrecked off South Africa in 1815, had a very large armament of 58 guns. This would have made her, in gun terms, the equivalent of a British fourth-rate ship (and the British navy in fact bought some Indiamen and fitted them out as fourth-rates). Here is a previous comment I wrote about "classes of vessels in the Age of Sail."

In any case, though, the number of guns is far less important than the number of sailors to serve the guns. In a battle, a warship had to have enough men to run out, point, load, and fire guns and simultaneously sail the ship, as well as pass ammunition, put out fires (literal and figurative), communicate with the captain and officers, etc. Indiamen had larger crews than comparable merchant ships but nowhere near the size of crews of warships, whether frigates or ships-of-the-line.

There was one incident during the Napoleonic period that saw a fleet of Indiamen beat off a French fleet, but such battles were vanishingly rare. Off Pulo Aor (near modern-day Singapore) in 1804, a squadron of Indiamen formed up in a line of battle and chased off a French fleet under Admiral Charles-Alexandre Linois; although Linois claimed he had been defeated by "eight ships of the line," in the words of N.A.M. Rodger, "At long range an Indiaman might pass for a small ship of the line, but the moment she tacked or fired the difference between 150 Lascars and 600 men-of-warsmen (to say nothing of the difference between an Indiaman's armament and a battleship's) would be instantly apparent..." (source).

tl;dr: Many merchant ships carried no guns at all, and some carried many; but the size of the crew was what made a sailing ship an effective fighting unit, and merchant ships did not have comparable manpower.

I hope this helps. Please let me know if there are follow-up questions.

Not very.

First of all, it is important to know that during this age the number of guns is not the whole story. If the gun is long, short or a carronade makes a huge difference. The longer the gun, the more accurate it is and the longer it can shoot. However, it is also heavier and slower to reload the longer it is. There were long guns, short guns and the shortest type which was the carronade.

The second factor is how heavy cannonballs the cannons fired. This was measured in pounds. A 24-pounder gun thus fired a heavier cannonball that would travel further and do much more damage than an 18-pounder gun.

Another factor is how heavily the ships were built. Military vessels were built out of oak, teak or mahogany - very tough and hard wood, while merchant vessels often were constructed out of other, softer types of wood. Military vessels were also built much more heavily to withstand gunfire than merchant vessels. Up to a meter of wood thickness was not uncommon in the larger vessels of war such as large frigates and men of war. Heavier built ships could carry heavier guns that merchantmen could not.

The most well-armed merchantmen during this era was the East Indiamen, large merchant vessels which travelled far and wide, often carrying spices, tea and porcelain from the East Indees and China to Europe.

We can compare for example the Swedish East Indiaman Göteborg from 1739 (of which a copy was built 2003), which displaced 1 150 tons and carried 30 guns -24 long 6-pounders on the battery deck and 6 long 3-pounders on the upper deck to the Swedish frigate HMS Camilla from 1784, which displaced 1 350 tons and carried 40 guns - 26 long 24-pounders on the battery deck and 14 long 6-pounders on the upper decks.

As you can see, on paper the ships look similar in size and armament, but when one studies the weight of the broadside (153 pounds for the East Indiaman versus 354 for the frigate) one can see that the military vessel is much more heavily armed. And when one adds the fact that the 6-pounders of the East Indiaman would be incapable of penetrating the sides of the frigate, while the 24-pounders of the frigate would probably be able to shoot completely through the East Indiaman, one can see that it is a one-sided fight.

Armed merchantmen could keep pirates (who often used small, fast and lightly built vessels) at bay and perhaps be used as blockade runners, blockade enforcers and commerce raiders, but they were at nearly all occasions unable to stand up to a purpose-built warship, even one of a substantially smaller size due to carrying lighter guns and being less heavily built.