I was doing some research on the empire and was quite astonished with the power they held at points in history. Although they never really were able to break into Europe. So to what extent would you say the Ottoman Empire became a European power?
What do you mean? They were knocking on Vienna's front door in 1688. Everything between Vienna and the Bosphorus is in Europe.
There is a tendency in European history classes (including the one I TAed for this year) to forget the Ottoman Empire existed. All of the assigned sources for this class were translations of French, German, and English (well, those weren't translations). It drives me bonkers, especially to see a tenured professor pretend Ottomans didn't exist. The textbook we used has exactly one reference to the Ottoman Empire in the index, consisting of two pages, half of which one is filled with a map.