Apostolos Vakalopoulos, Konstantinos Vakalopoulos and Dimitris Dimitropoulos have a 5-part series of books that describe the history of Byzantium and Greece from 1204-2002. The 2nd tome, "The Greek Nation 1453-1669" has many details on what you are looking for, and I highly suggest you take a look at the whole series if you are interested.
Basically, the Turks, like many other Muslim conquerors at the time, operated on a simple policy: "Surrender, convert and subordinate yourself and you get to keep your property. Resist and you will lose all that you own". Many of the rural and non-Constantinople Byzantine nobles converted and became Muslim, adapted Turk names. As a reward they got to keep their lands and property, while the Ottomans wanted them to stay exactly where they were, so they could help them rule their empire. The Ottomans didn't know much about running such a big empire and utilizing the existing Byzantine infrastructure was key to establishing control.
Meanwhile, those that resisted (noble or peasant) had their lands confiscated, which were then given as larger combined estates to the prominent Ottoman officers and courtiers. The people who lived inside those lands were turned into serfs basically. You have to remember here that the Byzantine Empire was not a feudal society as we imagine in France, England, Spain or Germany. Power was largely centralized. The nobles had a lot of land, but they didn't have many serfs, if any. Instead, most farmers were free men and owned land. So, if the land was taken from a noble he was usually executed. If it was taken from a peasant he was turned into a serf (although they weren't precisely serfs either). The peasants didn't have many qualms about accepting the Ottomans as their new overlords. This is because many saw them as a force that relieved them from the heavy Byzantine taxation.
Particularly the ones within the Catholic principalities and minor states (e.g. Athens) that were established after the 4th Crusade, were quite angry with the Catholics who mostly ruled with an iron fist and tried heavily to convert them. They also blamed them for the woes of the Empire, and they viewed them as opportunists, thieves, raiders and barbarians. Such was the hate against the Franks or Latins (as they were unilaterally called), that there were villages that outright revolted as the Ottomans approached and then asked their protection. In most of these cases, the local minor nobility and the peasants were given a few privileges at first.
Doukas in his "History" seems to concur this point. Doukas mostly focuses on what happened during the last decades of the Byzantine Empire. Basically what happened is that whatever the Ottomans took they followed a similar (but not as harsh) policy as I described above. However, the Byzantine nobles outside the Ottoman domains (those controlling areas on the Anatolian coast), started making deals with the Ottomans. They either started using them as mercenaries or straight up allied with them. Most of these were absorbed as Muslims and Turks peacefully as time went by. Those who didn't engage in such diplomacy with the Ottomans either converted under threat or were executed, but these were very few. There was a lot of political marriages happening (including a bride from the royal line being given to one of the Ottoman Beys/Sultans).
The nobility within Constantinople itself (those that survived the aftermath of the Fall), called Fanariotes after the suburb they mostly lived in (Fanari), were given asylum by the Sultan. Most of them were allowed to retain their faith and their Greek identity. They were given key administrative positions within the new empire and would help the Ottomans manage the Empire. They basically took the same positions they held before, only now they were the only ones who knew how to do their jobs. This gave them immense power, which they held up until the war of 1922. Their collaboration was rewarded with awards of land and titles. Notably, they were given the thrones of the Danubian Principalities (i.e. Wallachian, Moldavian and Bulgarian principalities that used to be vassals under the Byzantines and their relative autonomy came in exchange with them guarding the borders). We should note here, that Alexandros Ypsilantis, considered one of the major instigators for the Greek Revolution of 1821, was a Fanariotis (and openly Greek and Christian), who was the Prince of Moldovlachia (Moldavia & Wallachia). He used his power and title to organize a revolt in Moldovlachia. The hope was that they would instigate a revolt across the whole of the Balkans, but it ended up being quelled fast. However, this gave a valuable distraction that Ypsilantis' colleagues took advantage of to organize a Greek revolt in the Peloponesse, the other side of the Balkans.
The Orthodox Church, through the Patriarchate of Constantinople, had wielded immense power during the Byzantine era. The Ottomans recognized that if they couldn't control the Church, the Christians would never accept them as overlords. So, almost immediately, the Sultan issued a guarantee that the Church will not pay taxes to the state (a privilege held during the Byzantine era). He involved himself in the politics of the Patriarchate (ordering a couple executions in the process), and forced the new Patriarch to be approved by him before he was appointed. He also gave them a lot of other significant rights, while demanding stricter control and bribes. As a result, a large part of the upper clerical echelons (Patriarch, Bishops and Archbishops) started collaborating with the Ottomans almost straight away. They'd ask for donations from the faithful regularly that they'd use to bribe the Sultan and his Court to appoint them to the positions they wanted within the Church. Then they'd take advantage of their position, enriching themselves, while ensuring they kept the Christians under them complacent. I should clarify, I don't mean they were all bad, and there were many of them who were critical in maintaining the identity of the people they cared for and prevented their Turkification. But certainly a significant chunk of them were just there for their own monetary and political gain. The local churches and monasteries, free of a tax burden, were able to expand their land holdings significantly. Something that has great repercussions even today. (EDIT: I should note, that this was only true in the Balkans. Over in Anatolia, there were usually intense efforts to root out Christianity over the ages, which culminated prior and during the 1918-1922 war, and ended with the exchange of populations between Greece and Turkey after that war).
Having mentioned all this (and having talked about the peasants as well and Turkification), you should be aware that the Ottoman empire was a very... erratic government. Depending on who held the throne, one would observe their policies and stances shifting from highly accepting of Christians and non-Turks, to performing regular pogroms and forced conversions against them. Villages and areas allowed to retain their identity and religion for one decade, would then be put under sword and fire (alongside economic pressure through special taxation) the next decade, to force their conversion. (EDIT: One of the reasons this erratic behavior existed was because the Ottomans relied on the non-Muslim special taxations for internal revenue, so on one hand they wanted to convert everyone to being Muslim, and on the other hand they didn't wish to cripple their treasury). This didn't just affect peasants, it also affected the nobility that survived from the Byzantine times, as their own power also relied on land and property. They had the most to lose, so at times like these they were usually the first ones to convert. Their decision was made easier by the Patriarchate issuing a degree that Christians that converted to Islam would be forgiven as long as they retained their Christian faith within themselves and practiced it in secret.
As time went by, most major nobles were turkified, many minor nobles managed to survive intact in property and identity, while a plethora of new minor nobles emerged, to meet the demands of administration. Primarily, taxation and tax collection. These new ones were poor imitations of the nobility, merely bureaucrats holding power over the peasants residing in the same village as them. The way the Ottoman tax system worked, they were pushed to collaborate. Basically, the Sultan asked you that since your area had X people, he expected Y coins. But you aren't paid by the state directly. It is expected that from whatever you collect you'll take a cut and send the Sultan his tithe. So they would raise the tax rate from 10% to 20% (hypothetical numbers) so as to pay themselves. However, many of them were very important in the organizing of minor revolts and the 1821 Revolution later. Many others were extremely detrimental to the functioning of the new Greek state after the 1821 Revolution.
I hope you find this informative and helpful.