What kind of guns existed in the Ottoman Empire during Suleiman’s reign?

I'll try to answer your question, sorry if it doesn't satisfy you, though the period i cover ranged from the 16th to the early 18th century.

- Large/Siege Guns

This is what the Ottomans were famous for. From the 15th century they had manufactured large siege guns, but those manufactured in the 16th and 17th century were much smaller than the monster bombards of 15th century. 16th century Ottoman military specialists considered 8 to 22 okka calibre (1 okka=1.28 kg) guns firing projectiles of 10-27 kg to be suitable for campaigns and sieges

Kale-kob

Cannons of 14 to 16-okka calibre that fired 17 to 20 kg of projectiles are specifically referred to as kale-kob (fort-smasher). Later on in the 17th Century, there were also smaller 12-okka calibre guns that fired 15 kg projectiles. These cannons can be compared to European culverins and siege cannons

Şayka

According to Evliya Çelebi, şayka are guns that are too large to be carried by humans. In campaigns, they had to be slid through sleds. The name şayka derives from the Slavic chaika "seagull" boats that were used to defend rivermouths. The Ottomans differentiated between large, medium, and small şayka guns often without specifying their calibre. The shortest pieces were 176, 198, and 264 cm long, the medium one 380, 332, and 352 cm long, while the large ones 396, 440, and 462 cm long. While the 176 cm long 5-okka şayka guns can be considered small, the 264 cm long 44-okka piece even though relatively short is one of the largest şayka so their size and calibre is greatly varied.

Balyemez

Balyemez were large siege guns similar to şayka, though most of the time they resembled small and medium şayka. Evliya Çelebi mentioned balyemez guns of 25, 30, 40, 50, and 60-okka calibre. He also noted that were only 4 largest 60-okka balyemez in the entire empire, and those were fortress guns. These cannons correspond to the largest European bombards and were mostly relics of the 15th century, mostly used as siege and fortress guns. Those produced in later era were much smaller. In 1686 for example, the foundry only casted two balyemez guns of 11 and 14-okka

Bacaloşka

Perhaps the most popular and widely used siege guns, equivalent of European basilisks. Small bacaloşka ran from 1 to 11-okka firing projectiles of 1 to 14 kg while larger ones ran from 14 to 23-okka firing shots of 17 to 28 kg. Short pieces were 198 to 220 cm long, while larger ones were usually 396 to 440 cm long. The largest piece in the 1520s weighed more than 11 tons. However, these were the rarity because the average weight of bacaloşka between 1522 to 1526 were around 4.1 tons. As mentioned, these were the main siege guns of the Ottoman army. For example there were at least seventeen bacaloşka, mainly 14 and 16-okka deployed deployed during Süleyman's siege of Szigetvar on 1593. It appears that most bacaloşka on campaign were medium or small, ranging from 11 to 22-okka while larger siege guns were often şayka or balyemez

- Medium Field Guns

Kolunburna

These were light field guns, the equivalent of culverin of Europe. Like culverins, these varied in size. 16th century inventory mentioned kolunburna with 1.5 to 7-okka calibre firing 2 to 9 kg projectiles. 17th century inventory recorded pieces from 2 to 10-okka calibre, and occasionally 11, 14, and 16-okka calibre firing 2 to 20 kg shots.

Darbzen

These were the most popular and widely used medium guns in the campaign. Even though the meaning is "battering gun" and large number of them did indeed used in sieges, these were also deployed in battles. There were three types of darbzen, small (küçük), medium (miyâne) and large (şahı). In a 16th century source, small darbzen fired balls of 920 g, medium ones 1.23 kg, and large ones 2.5 kg. Generally, darbzen used in campaigns were really light, for example 625 darbzen weighing on average 162 kg were cast in Istanbul. Of course there are larger ones, forty-six large darbzen cast in 1604 weighed around 540 kg. Many guns of this type were used by the Ottomans in campaigns because of they're relatively easy to transport. A significant number of darbzen were deployed in the battle of Mohacs, 280 large darbzen were used in the siege of Szigetvar, and 300 darbzen were cast for the 1596 Hungarian campaign.

Şahı

Ottoman sources usually refer to şahı for a larger version of a gun, however they also use the term for a long, but small gun. Inventories from the 17th century listed 242 to 300 cm long şahı gun. The majority of them were small guns firing shots from 150 grams to 1.8 kg in weight. The weight of this guns varied. A 0.5-okka şahı gun weighed around 169 kg, while a 1-okka gun weighed around 325 kg. Occasionally we can find larger şahı guns with 4 to 6-okka calibre.

- Small Pieces

These were very small pieces, often used as naval or castle guns. saçma is one of the smallest Ottoman guns, and as the name suggests fired grapeshots. The average weight of the saçma was around 36.5 kg. These were used as naval guns, for example 85% of guns used by the ships of the Ottoman Black Sea Fleet in Özi on 1698 were iron-cast saçma guns. Eynek is an even smaller gun. Sixty-two eynek cast in 1695 weighed only 22.7 kg on average, while those cast in 1697 weighed just 11.5 kg. They were mainly used above river ships like the ships of Danube Fleet. Another small gun, Prangi usually fired shots of 150 g. They can be easily cast in local foundries and are mainly used as castle guns. Lastly, Şakaloz is a very small gun used in castles. These are the equivalent of Hungarian hook-guns (szakallas). These fired projectiles as small as 31 to 37 grams. For comparison, some Spanish and Ottoman musket bullets weighed more than 50 grams. Because of this, they were mostly used as close-range anti-personnel weapons against besiegers. They were ubiquitous in castles, for example in 1536 there were 900 şakaloz in the castle of Semendire

- Muskets

Generally, the Ottomans used the matchlock musket (fitilli tüfek) From the late sixteenth century onward, Ottoman troops also started to use flintlock muskets (çakmaklı tüfek), though matchlocks remained to be favourite for quite some time because of the unreliability of the early flintlocks. The length of these guns varied, The guns used in the Iraq campaign in 1553, for example, fired projectiles of 15 grams and were 88 cm to 110 cm long. The 2,498 guns that were manufactured in the imperial workshops and sent to the armory in 1555 were registered as being 88 cm long and firing projectiles of 12 grams. Muskets in the Topkapi are 115 to 140 cm long, weigh 3 to 4.5 kilograms, and bore diameters of 11, 13, 14, or 16 mm. Additionally there were also large and heavy trench guns called metris tüfeği to be used in sieges. It had a 130-160 cm long barrel and bore diameters of 20 to 29 mm, though there are larger ones that bore diameters of 35 and 45 mm.

Sources:

Guns For The Sultan and Firearms and Military Adaptation by Gábor Ágoston