Hey OP, I'll do my best to answer my question. I'm more at home in the middle Byzantine period, but I think I can give you some pointers for further reading and a brief summary of events. Keep in mind that I am mostly writing from the Byzantine perspective of things, as I am not too knowledgeable about the Ottomans

Something I want to stress first is that Constantinople was at this age a city in decay, and more a collection of seperate villages within the city walls then truly one, large city. Large swathes of the city were abandoned and the number of inhabitants had plummeted to +/- 100.000 from it's peaks of 1.000.000 in the Komnenian and Macedonian period.

Sir Runciman says that some of the 'villages' within the city were more then a hundred meters apart from eachother, and the 'village heads' of these sometimes acted independently from the emperor. Some of these village heads surrendered to the Ottomans, and their neighbourhoods were then spared. Those who did not surrender though, lost their freedom and were often enslaved by the Turks.

Parts of the city were sacked, especially many churches, but the devestation was nothing like the crusaders had unleashed upon the city in 1204. The imperial palace was sacked as well. An interesting note is that not all of the churches were sacked, and some were even retained in good state. The Hagya Sofia was claimed by the Sultan, but the church of the Holy Apostles was retained by the Orthodox by the sultan's grace, and turned into the seat of the Patriarchate.

Mehmed was (relatively) graceful to the city and it's inhabitants, because he didn't want to inherit a ruined and deserted city, but wanted to turn Constantinopel into his imperial capital. This is why the city was not laid into ashes and most of it's inhabitants were allowed to stay if they wanted to do so. It was in Mehmed's interest to keep the city functioning because of it's strategic and symbolic value, and the Turks (at first) needed the support of the local Greeks to keep the wheels of the city turning. All in all the city was kept relatively well and it would take some years before large changes and rebuilding projects were started.

Sources: -Sir Steven Runciman; The Fall of Constantinople 1453

-Cyril Mango; The Oxford History of Byzantium

-Kritovoulos; History of Mehmed the Conqueror