You would probably approve of slavery as you understood it, but you might not approve of the type of chattel slavery practiced in the West Indies and elsewhere in the New World. Certainly slavery in the Ottoman Empire could be as brutal as anywhere, but there were gradations, and it was not necessarily the kind of race-based, hereditary slavery that developed on plantations in the Atlantic World.
The Ottoman Empire actually had a rather unique attitude towards slavery and how it incorporated it into its society and administrative structure, as #5 suggested. Slaves were deliberately sought out to be trained as administratives in the structure of the Ottoman Empire and therefore slavery is certainly rather different than we would expect given our ideas of what slavery involves. It was a good thing in some ways to be a slave working for the Ottoman Empire.
If you are the Ottoman Empire, prior to the 19th century, slavery was of the utmost importance. Slavery in the Ottoman Empire has been recorded to have existed as early as the 14th century (a period in time where both Murad I and Murad II ruled). In fact, Murad II opened the first market where slaves were sold and traded.
In the early Ottoman empire, not only would you be in favor of slavery, you would depend upon it for limiting corruption in government. Certain slaves, bought from other lands for the purpose, were raised to take on official positions in the political structure. This controlled government corruption because (1) the slaves felt gratitude for how they were treated and for their opportunities thus also felt great loyalty and (2) they had no past allegiance to leaders or policies or sectors of the empire.
Although slavery was crucial in the Ottoman Empire, at the beginning of the 1800s the Ottoman Empire outlawed slavery of white men. They still enslaved women until about a hundred years later. By that time there were fewer non-sexual slaves because European countries frowned upon the practice of slavery.
This is an excellent question. We normally think of Europeans and Americans as slave owners and slave traders, but the Ottoman empire had a major involvement in holding Europeans and other whites as slaves. Christians were often terrified of becoming slaves owned by Muslims. The link below may be useful to you.
You haven't told us what period you are in here. Slavery was a huge part of the Ottoman system. There were even whole army units made up of elite slaves called janissaries. Slavery continued in the Ottoman Empire well into the 19th century. The slave trade was abolished in the 1850s but there was no emancipation of slaves in general.