Sorry for the late reply, I'm a Thai lurker on this subreddit and I found this by chance through browsing 'new'.

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Siam, or Krung/Muang Thai (literally meaning 'land of the Thai') as it was known to local inhabitants (Siam is a Western name for it we picked up during the late 18th century after Westerners kept calling us Siamese) was indeed a regional power from the late 15th century onwards with the Ayutthayan Kingdom, and perhaps even earlier if you consider Sukhothai, which annexed most of the western Chao Phraya basin from it's former Khmer overlords during the decline of the Khmer Empire. At the largest extent of it's territory, Ayutthaya controlled much of northern Laos, the Kingdom of Chiang Mai/Lan Na (modern day northern Thailand), down to the northern Malay states of Pattani (which remains a part of Thailand today), Kelantan (known under the Thai name of Klangtang), and also had control of Marit (Mergui), Twai (Tavoy) and various different parts of Cambodia, most notably being Phra Tabong (Battambang), and, in a final insult to the Khmer Empire's legacy, large parts of it's old capital of Angkor was renamed to Nakhon Siam (Siem Reap).

The Siamese military was one of the strongest in the region, because Ayutthaya itself was a very culturally diversified city - contemporary French scholars compared it in size to Paris, calling it the 'Paris of the East' for it's size, and the Portuguese called it 'the Venice of the East' due to it's trade power and various canal networks (traditionally Thai people preferred to travel via boat). Therefore, various different peoples and adventurers lived in the city, and the Krom Asa (Volunteer Corps) were a section of the Royal Siamese Army that consisted of various mercenaries, notable mentions include, Japanese bodyguards favoured by King Ekatosarot (brother of Naresuan), and Portuguese musket mercenaries. However, Ayutthaya's royal history was plagued by various civil wars because traditionally, Thailand never had a clear line of succession until the late 19th century when King Rama V created the office of Crown Prince to replace the increasingly obsolete Uparat, or 'Front Palace'. Therefore, the country would often be torn apart in civil wars, and every time there was one, the Burmese in particular would often swipe in and grab territory only to have it taken back by the new King - Mergui (Marit) changed hands so often that the population was known to contemporary Western sources as half-Thai half-Burmese. Ayutthaya was sacked twice - once in the reign of King Naresuan, and the final time in the reign of King Ekatot, which constituted the final fall of the kingdom.

Siam was reestablished as a state by King Taksin of Thonburi, who established the new capital at the short-lived city of Thonburi, and his right-hand-man and best general, Chao Phraya Chakri, who would later become King Rama I, and founder of the of the Chakri dynasty on the opposite bank of the Chao Phraya river at a former trading outpost granted to the French during the reign of King Narai the Great called Bangkok. Bangkok was later renamed to Krung Thep later in the Rattanakosin era (as Chakri rule-era came to be known), but Westerners still refer to it as Bangkok today.

If you wanted an indepth view of every Chakri monarch (and indepth information on Ayutthayan monarchs before), I suggest reading the very well-written 'Lords of Life' by HH Chula Chakrabongse, but I'll try to sum up every reign in a couple sentences.

Rama I (King Buddha Yotfa Chulaloke):
Established the new capital of Bangkok, and the Palace of the Emerald Buddha within the Grand Palace. Returned official law to Siam after the great wars that left the country devastated (see Three Seals Law), and overall reign was oriented at legislation and reconstruction

Rama II (King Buddha Loetlat Nabhalai)
The 'Shakespeare-like' King of Siam - greatly loved arts and drama, and wrote various plays that remain today. His reign is known as the golden age of Thai culture and arts

Rama III (King Nangklao)
The 'Merchant-King' of Siam, during his reign Siam became the regional economic powerhouse - he banned opium permanently after seeing what happened to China, one of the reasons why the trade never prospered in central Thailand unlike other Asian countries in the region. It was during his reign official relations were reestablished with Western countries. His reign made Siam so rich that the treasury was still overflowing in the reign of his grand-nephew King Rama V - something that would come in very useful later.

Rama IV (King Mongkut/Chom Klao Chao Yhu Hua)
King Mongkut was very unlike how the Western play depicts him - he could speak English very well (along with nine other languages excluding Thai), and was very open-minded to liberal reforms in the country, but was very much the king of a country with highly conservative nobles. He desired for his children to all be Western-educated so he hired the very infamous Anna Leonowens to teach them English. What you need to know is she taught his children English, left shortly before he died and never returned to Siam. Everything else is made up by Broadway and the governess herself, who made a fine living in post-Civil War USA writing books about being responsible for freeing slaves. His reign was notable for the abolishment of slavery, and he was a renowned astronomer, but due to his elderly age upon inheriting the throne, and due to an unfortunate contraction of malaria, he passed away too soon leaving his 15-year-old son to inherit a kingdom ruled by conservative nobles under the Bunnag family (the patriarch, Chao Phraya Suriyawongse was the regent, and the most powerful man in Siam) until he was able to assert himself and his authority a decade later.

Rama V (King Chulalongkorn the Great/Chula Chom Klao Chao Yhu Hua)
One of the most beloved monarchs in Siamese history, King Rama V is credited with the modernization of the nation from what was essentially a feudal-slightly industrialized series of vassal towns to a modern, united Thai state. All his sons were Western-educated, sending some to study in all the great Western powers of the world, notable examples being King Rama VI who was an Oxford graduate, HRH Prince Chakrabongse who was educated in imperial Russia, or HRH Prince Paripatra who was German-educated. During his reign, he fostered relations with Tsar Nicholas II, and played the two border powers, France and Britain against each other with remarkable political flair, but Thailand still ended up losing the right side of the Mekong and most of Cambodia to the French during the Paknam Crisis, and various areas like the Shan States to Britain. This marks the end of Old Siam, and I would regard the reign of King Rama VI onwards as modern Thai history.

If you have any particular queries, I am most happy to assist.

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Sources:
"A History of Thailand" - Christopher Baker, and Pasuk Phongpaichit
"Lords of Life" - Chula Chakrabongse
"Thailand's Political History" - Jan Terwiel

By the way, all the books I sourced are all excellent and unbiased retellings of Thai history - if you're interested, I greatly recommend these three.