It can be tricky getting into the operating room, and more so if you want to scrub. You can become an operating room circulator with an internship. The recommended length is 6-9 months, though I tend to see local hospitals offering more like 3-4, because they don't teach nurses to scrub. Because many hospitals that have nursing schools also have scrub tech schools, it can be very hard to find someone who will actually train you to scrub.
Working in the operating room room can be a high-stress, grueling specialty. If you are circulating, you run your pants off. If you scrub, you're standing all day long. There's a lot of call and you work most days of the week. There are exceptions, of course, but it's a lot to consider. Regardless, I wouldn't go to ST school. If anything, go get a surgical assisting degree/ diploma.