If I recall correctly, the second placement exam was considerably more difficult than the first, and it would take about 90% on the second exam (with a perfect score on the first) to place into 150s. The standard calculus sequences start right where high-school left off, delve into a fair number of proofs, and rely on a clear understanding of a few key concepts, so the placement test is designed to smoke out students whose mastery of pre-calculus material is anything less than perfect.
The tutorial may be more useful than expected. Most UChicago first-years found hand-holding unnecessary in high school, but even the basic math sequences move at a fast clip in college. Having a chance to hear common questions answered in detail is infinitely more helpful than piecing together an answer based on the textbook (which isn’t very good) and Khan Academy. First Year taught me to take notes religiously, but I still went to problem sessions whenever I could.
As for the importance of pre-registration rankings, the standard math sequences are one area where that won’t matter too much. Introductory classes like Elementary Functions and Calculus (130s) or Calculus (150s) are usually taught by grad students who move on after a year or two, so picking a section by the professor’s evaluations is hit-and-miss at best. Every year, a few sections dwindle to a handful of students as it turns out the grad student is awful, more are full to the brim every quarter because the instructor is great, and most turn out fine - with students switching in and out as their timetables change. Scheduling is the only known quantity, so I’d suggest using the registration period to make schedules work and not worrying too much about the instructor.
Also: keeping in touch with the instructor always helps. Exam marking is generally pretty clear-cut - an answer or a step in the working is either correct or incorrect - but the good instructors will go above and beyond for students who communicate. Case in point: I was a regular at problem sessions and asked lots of questions by e-mail. After I had a nasty bout with the flu and missed several lectures in the run-up to finals, my instructor spent something like a dozen hours getting me up to speed and helped me salvage the quarter. If I’d been face in the crowd #29, or shown up at his door two days before finals, I might be retaking that class this winter.