There are a lot of different motivations as you might expect. Most of the controversy from the Ghazi hypothesis comes from its assertion that Osman I Ghazi (the first Sultan) led an entirely new movement or that the Ottomans swept up onto the scene. It is true of course that there was religious motivation to fight wars, but the Ottomans were just one of many Turkic beys in Anatolia. They also had the foundations of Seljuk Turk civilization and institutions that they tapped into, which really helped consolidate the early sultanate. One important point that people miss about Ottoman-European wars is that the Turks did not see the Europeans as their main enemies for religious reasons like we might expect. The Shiite Safavid dynasty in Iran were their main enemies, as the Ottomans saw them as heretics. Christian European states were foes but for more conventional political reasons.

After the Interregenum period brought on by Timur, you start to have more focused Ottoman conquest into the Balkans. There were a few reasons for this I will sketch out:

1. The empire had a constant flow of nomadic Turkmen coming in from Central Asia. The state tried to forcibly settle them and also pushed them further out into Balkans. This de-facto expanded the reach of the Ottoman Empire into territories that they didn't fully control. Part of the military until the late 16th century was the akinji (raider) corps made up of troops from this nomadic Turkic background.
2. Simple opportunity: when the Ottomans were rising in the fifteenth century, the post-Byzantine, Orthodox Balkans were between the Catholic Kingdom of Hungary and the Ottomans. Many Orthodox Balkan peoples, both commoner and elite, would rather be under Muslim control than Latin Catholic rule. The nobility were typically subsumed into the Ottoman timar land-holding system. Under Suleiman, part of his motivations for expanding into Hungary was a need to prove himself after his father, Selim I, conquered the Muslim Holy Cities. He was able to do this because he had an alliance with the king of France, who had the Habsburgs tied up fighting for control of Italy. This gave him the opportunity move into Hungary, which was a rich agricultural region and had strategic value from the Danube River.
3. The need for timar system expansion: the timar system was, until the seventeenth century, the foundation of the Ottoman military-political order. Timars were awarded for service in war like a feudal title and the holder had rights to the land. Unlike European feudalism, it was non-hereditary. Every time the empire went to war the timar holders had to go to war and made up the timariot cavalry. They also had to bring retainers and fund their own warfighting costs. This is what gave the Ottomans a major numerical advantage over European armies, who often had paid mercenary forces. However, to keep this system going the Ottomans had to conquer new territory semi-regularly which became unsustainable during the late sixteenth century.

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M. Fuad Körprülü, The Origins of the Ottoman Empire, trans. Gary Leiser (Albany: State University of New York Press, 1992)

Halil Inalcik, The Ottoman Empire: the Classical Age 1300-1600 (London: Phoenix Press, 2000)

Nikolay Antov, The Ottoman “Wild West:” The Balkan Frontier in the Fifteenth and Sixteenth Centuries (Cambridge: Cambridge University Press, 2017)

I have more detailed/technical sources I can recommend as well but these are the easiest to find for non-academics.